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Find the square root of 8-2√5​

Answers

Answer 1
Answer:

Answer:

The square root of 8 - 2√5 is

\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }

Hope this helps you.
Answer 2
Answer:

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

Related Questions

1. Julia's goal is to run faster than two of her friends in an upcoming6.2-mile race. The table shows the results of the last race that eachrunner finished. Assume they each run the race at the same ratethey ran their last race. Complete the table. Who will finish firstamong the three friends, and by how much time will she beat thesecond-place finisher?RunnerJuliaHazelMekenaLast RaceDistance(mi)856Last RaceTime(min: sec)62:0039:1046:00Rate(min:secper mi)Time for6.2 Miles(min: sec)
Put in order from least to greatest. 0.08, -0.38, - 3/5, - 0.04
Please help please please help
From 1985 to 2007, the number B B of federally insured banks could be approximated by B ( t ) = − 329.4 t + 13747 B(t)=-329.4t+13747 where t is the year and t=0 corresponds to 1985. How many federally insured banks were there in 1990?
how can you determine that the polynomial function does not have any zeros with even Multiplicity? Explain.​

A mother wants to invest $6000 for her children's education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $360, how much money was invested at each rate?

Answers

0.04x+0.07(6000-x)=360
0.04x+420-0.07x=360
0.04x-0.07x=360-420
−0.03x=−60
X=60/0.03=2,000 at 4%
6000-2000=4000 at 7%

What is the y intercept of the line -9x+3y=18

Answers

y = 6

hope this helps

Answer: (0, 6)

Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

Question is −9x + 3y = 18

Our first step would be is to find y which will be done by 3y = 18.

Part 1

Step 1: Enter y equation.

3y = 18

Step 2:Simplify.

y = 6

Now that we have our y, we need to find our X. We can do this by plugging in y, which is 6 into the equation to find X.

Part 2

Step 1: Enter the X equation by plugging in y.

−9x + 3(6) + 18

Step 2:Simplify.

−9x + 18 = 18

Step 3:Simplify.

−9x = 18 − 18

Step 4:Simplify.

(-9x)/(-9) = (0)/(-9)

Step 5: Simplify.

x = 0

Because 0 is our X coordinate and 6 is our Y coordinate, we will need to have the X and Y coordinates in parentheses, So (x, y) would be (0, 6). And there you go we have the answer. Good luck!

~I hope I helped you! :)~

3n-5=-8(6+5n) in distributive property

Answers

Using distributive property we can expand the expression as

3n - 5 = -8 x 6 + (-8) x 5n

To apply the distributive property to the equation

3n - 5 = -8(6 + 5n), we need to distribute the -8 to the terms inside the parentheses.

Using the distributive property, we have:

3n - 5 = -8 x 6 + (-8) x 5n

Simplifying further:

3n - 5 = -48 - 40n

Now, we can continue solving the equation using the simplified form as

3n + 40n = -48 + 5

43n = -43

n= -1.

Learn more about distributive property here:

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Answer:

n=-1

Step-by-step explanation:

3n-5=-8(6+5n)

3n-5=-48-40n

add 40n to both sides

43n-5=-48

n=-1

Suppose an airline policy states that all baggage must be box shaped with a sum of​ length, width, and height not exceeding 96 in. What are the dimensions and volume of a​ square-based box with the greatest volume under these​ conditions?

Answers

Answer:

Step-by-step explanation:

As the base is a square so the length is a, width is a and the height is h.

According to the question,

a + a + h = 96

h = 96 - 2a     .... (1)

Volume of the box, V = length x width x height

V = a x a x h

V = a² (96 - 2a)    from equation (1)

V = 96a² - 2a³

Differentiate both sides

(dV)/(da)=192 a -6a^(2)

Now put it equal to zero.

192 a - 6a² = 0

a = 32 in

h = 96 - 2 x 32

h = 32 in

Thus, the length and the width os teh base is 32 in and the height is 32 in.

Final answer:

A square-based box with the greatest volume under a restriction of the sum of length, width, and height not exceeding 96 inches must have each dimension equal to 32 inches. Therefore, its volume will be 32x32x32 = 32,768 cubic inches.

Explanation:

A square-based box with the greatest volume that can fit the airline's restrictions would have each side (length, width, height) be exactly one third of the total permitted sum, namely 32 inches each, because the volume of a square-based box (a cube in this specific case) is calculated by cubing the edge length. This is due to the nature of a cube, where all sides are equal.

So, the volume of the box would be 32in x 32in x 32in = 32,768 cubic inches. This is the maximum volume because the mathematical principle that for a given sum S of width, length & height, a cube always takes up the most volume.

Learn more about Optimization in Mathematics here:

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What is this equation????
m=y2-y1\y2-y1​

Answers

Answer:

Are you sure it ia not x2 - x1 in the denominator?

Answer:

x=2-y

Step-by-step explanation:

Root (2,0)

Vertical intercept (0,2)

Three students were given the expression shown and were asked to take a common factor out of two of the terms. Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent.

Answers

Answer:

Step-by-step explanation:

Given: 4 - 9x +21

Factorizing this expression, we have;

              4 -3(3x - 7)

i. Chang's expression: 4 - 3(3x + 7)

This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 -9x -21

ii. Benjamin's expression: 4 + 3(3x + 7)

This is not an equivalent expression, because by expansion of the bracket, the expression gives: 4 +9x +21

iii. Habib's expression: 4 + 12x

This is not an equivalent expression, because the expression is not related to the given question

Comparing the three student's answers with the appropriate expression, none of the student's is an equivalent expression.

This expression that is  equivalent to the given question is;

            4 -3(3x - 7) = 4 -9x + 21

Answer:

1,2,4

Step-by-step explanation:
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