Question

Find the value of √256 .​

Answer 1

Answer:

route to 56 is equal to 16 square

Answer 2

Given to find the square root of 256

Solution :-

First write them into product of prime numbers by using prime factorisation method

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:256\:\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:128\:\:\:}} \\\underline{\sf{2}}& \underline{\sf{\:\:64\:\:\:}} \\\underline{\sf{2}}& \underline{\sf{\:\:32\:\:\:}} \\\underline{\sf{2}}& \underline{\sf{\:\:16\:\:\:}} \\\underline{\sf{2}}& \underline{\sf{\:\:8\:\:\:}} \\\underline{\sf{2}}& \underline{\sf{\:\:4\:\:\:}} \\\underline{\sf{2}}&{\underline{\sf{\:\:2\:\:\:}}} \\ \underline{\sf{}}&{\sf{1\:\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

So, 256 can be written as 2 × 2 × 2 × 2 × 2 × 2 × 2 ×2

Take a pair and write them

256 = 2² × 2² × 2² × 2²

$\sqrt{256} = \sqrt{2 {}^{2} \times 2 {}^{2} \times 2 {}^{2} \times 2 {}^{2} }$

$\sqrt{256} = \sqrt{(2) {}^{2 + 2 + 2 + 2} }$

$\sqrt{256} = \sqrt{2 {}^{8} }$

$\sqrt{256} = \sqrt{(2 {}^{4}) {}^{2} }$

$\sqrt{256} = {2 {}^{4} }$

$\sqrt{256} = 16$

So, square root of 256 is 16

____________________

Know more :-

Square number :- Square number means which can be written as product of two equal numbers

Cube number :- Cube number means which can be written as product of three equal numbers