Question

use long division method find the square root of 16129

Answer 1

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The answer is 127



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Answer 2

The square root of $16129$  is $127$

Step-by-step explanation:

Given,

Use long division method find the square root of $16129$

Group the number in groups of $2$ starting at the back,

So $1\,16\,29$

Find an approximate square root $x$ of the first group,

Such that $x\leq$ the first group

In this case $x=1$.

Square it and subtract from the first group, giving $0$.

To this remainder join the next group: $061$.

Now find the largest number $y$,

Such that $y(20x+y)\leq 61$. $y=2$.

Subtract $y(20x+y)=44$ from $61$ to get $17$.

Join $y$ to $x$ this to get your new estimate $x=12$. Bring down the next group of two digits $1729$ and find the largest number $y$ such that $y(20x+y)\leq 1729$ and $y=7$

Subtract $y(20x+y)$ from $1729$, bingo that’s $0$

Join this $y$ to $x$ to get your final result $x=127$

So, The square root of $16129$  is $127$