square root of 10 4/7

Question

Can you please help me figure out what the square root of  10 4/7 is please?

Answer 1

Hello, Melica

 

What is the sq. rt. of 10 4/7?

 

This is a mixed number,so what I am going to do it make it into an improper fraction.  You might recall that in order to make an mixed number into an improper fraction. You

1) multiply the denominator times the whole number. This will be 10* 7= 70

2) add to this sum the numerator. So, you add 70+4= 74. This becomes the numerator of the improper fraction.

3) keep the same denominator. We end up with 74/ 7

 

But that is not the question.  This is not a perfect square, so unless you have a college degree in math, you will need to use a calculator to find the square root of 74/7. Or you might estimate.  74/7 is about 10. 6

So, its square root lies between 3 and 4.

If you are allowed to use a calculator enter 74/7 and the press the radical sign.  Sq. rt. 10.5714 becomes 3.2514.  So, the answer rounding to the hundredths place value is 3.25.

 

Good luck,

 

D. Y. Taylor

 

Answer 2

I'm assuming you cannot use a calculator, so let's do our best to estimate.

 

First, let's change to an improper fraction. 

 

10 x 7 = 70 

70 + 4 = 74.

 

Keep the same denominator -> 74/7.

 

Now, find the square root of both the numerator and denominator.

 

Since neither 74 nor 7 are perfect squares, we need to find approximate squares.

 

8^2 = 64

9^2 = 81.  Thus, sqrt(74) is about 8.5

 

2^2 = 4

3^2 = 9.  Thus sqrt(7) is about 2.5

 

So, sqrt(74/7) = 8.5/2.5

 

We cannot leave decimals in a fraction, so multiply top and bottom by 2.

 

8.5 x 2 / 2.5 x 2 =

17/5 

 

Chance back to a Mixed Number.

3 2/5

 

(The real answer is about 3 1/4, so this is a pretty reasonable estimate)