Question

Estimate the value of the following square roots to the nearest whole number :
$\sqrt{800}$
​

Answer 1

The estimated value of the $\sqrt{800}$  is 28

Step-by-step explanation:

To Estimate the value of the square roots to the nearest whole number

first we have to find the value of square root of the given number

here ,

we need to find the value of $\sqrt{800}$

using the prime factorization

800 = 2×2×2×2×2×5×5

taking square root both sides

we get

$\sqrt{800}$ = $\sqrt{2\times 2\times2\times2\times2\times5\times5}$

now,

$\sqrt{800}$  = $2\times 2\times5 \times\sqrt{2}$

$\sqrt{800}$ = $20\sqrt{2}$

taking the value of $\sqrt{2}$ = 1.414

$\sqrt{800}$  = 20×1.414

$\sqrt{800}$  = 28.28

estimated value of 28.28 = 28

hence,

The estimated value of the $\sqrt{800}$  is 28

#Learn more:

Estimate the value of the following square root to the nearest whole number square root 440

https://brainly.in/question/14713128

Answer 2

Hi . .... ...

Factors which will remain inside the root are :

2 = 2

Factors which will be extracted are :

400 = 2^4 • 5^2

Factors which will remain inside the root are :

2 = 2.

We do this by dividing their exponents by 2 :

20 = 2^2 • 5

The simplified SQRT looks like this:

20 • √(2)

Answer = 20 • √(2)

and when we simplify then it

approximately 28.28427

hence we can said 28 is as answer.

i hope it helps you.