Question

Find the square root of 100 up to 2 decimals.

Answer 1

Hint: First of all, get the factors of 100. We can see that 100 is an even number, so its one factor is 2. Now, we can see that 100 can be written as \[2\times 50\] . We can see that 50 is an even number, so its one factor is 2. Now, we can see that 50 can be written as \[2\times 25\] . Now, 25 can be written as a product of 5 and 5. We have to write 100 as the product of these factors. Now, solve it further.

Complete step-by-step answer:
According to the question, it is given that our number is 100 and we have to find the square root of 100 up to 2 decimals.
We have to get the value of \[\sqrt{100}\] .
First of all, we have to find the factors of 100 and then only we can get the square root of \[\sqrt{100}\] ………………….(1)
We can see that 100 is an even number and we know that even numbers are divisible by 2. So, 100 is also divisible by 2.
\[100=2\times 50\] ………………….(1)
Therefore, 100 can be written as \[2\times 50\] .
Now, we need the factors of 50.
We can see that 50 is an even number and we know that even numbers are divisible by 2. So, 50 is also divisible by 2.
\[50=2\times 25\] ……………………..(2)
Therefore, 50 can be written as \[2\times 25\] .
Now, we need the factors of 25.
We can see that 25 is divisible by 5.
\[25=5\times 5\] ……………………(3)
Therefore, 25 can be written as \[5\times 5\] .
Using equation (2) and equation (3), equation (1) can be written as,
\[100=2\times 2\times 5\times 5\] ………………….(4)
We have to find the value of \[\sqrt{100}\] ………………………….(5)
Putting the value of 100 from equation (4) in equation (5), we get
\[\sqrt{100}=\sqrt{2\times 2\times 5\times 5}=2\times 5=10\]
So, the value of \[\sqrt{100}\] is 10.
But we have to square the root of 100 up to two decimal places. So, we have to add two zeros after the decimal in number 10.
Hence, the square of 100 up to two decimal places is 10.00.

Note: We can also solve this question without finding out the factors. We know that the square of 100 is 10.
So, \[\sqrt{100}=\sqrt{{{\left( 10 \right)}^{2}}}={{\left\{ {{\left( 10 \right)}^{2}} \right\}}^{\dfrac{1}{2}}}\] ……………………….(1)
We know the formula, \[{{\left\{ {{\left( x \right)}^{m}} \right\}}^{n}}={{\left( x \right)}^{mn}}\] .
Now, using this formula to solve equation (1), we get
\[{{\left\{ {{\left( 10 \right)}^{2}} \right\}}^{\dfrac{1}{2}}}={{\left( 10 \right)}^{2\times \dfrac{1}{2}}}={{\left( 10 \right)}^{1}}=10\] .
So, the value of \[\sqrt{100}\] is 10.
 But we have to square the root of 100 up to two decimal places. So, we have to add two zeros after the decimal in number 10.
Hence, the square of 100 up to two decimal places is 10.00.