Question

What is the square root of 625?
(a). 62
(b). 25
(c). 12
(d). 66

Answer 1

Hint: A square root of a number is a value that, when multiplied by itself, gives the number. Recall the method to find the square root by long division and find the value of the square root of 625.

Complete step-by-step answer:
The square root of a number is another number that produces the first number when it is multiplied by itself. For example, the square root of 25 is 5 because 5 multiplied with 5 is 25.
Sometimes, it is obvious to find the square root of a number, usually a smaller number but other times, the number might be big and we need to use a method called long division to arrive at the answer.
In this problem, we need to find the square root of 625.
As the first step in long division, we need to pair the digits from the right.
Hence, we pair 2 and 5 as 25, and the digit 6 has no digit to pair with.
\[6{\text{ 25}}\]
Next, we need to find the largest integer such that its square is less than the first digit.
We know that \[{2^2}\] which is 4 is less than 6.
\[\begin{gathered}
  2\mathop{\left){\vphantom{1{6{\text{ 25}}}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{6{\text{ 25}}}}}}
\limits^{\displaystyle \,\,\, 2} \\
  {\text{ - }}\underline {\text{4}} \\
  {\text{ 2}} \\
\end{gathered} \]
Now, we bring the next pair down and the number becomes 225, we now need to find a number such that 4x multiplied with x gives 225.
We know that 45 multiplied with 5 gives 225.
\[\begin{gathered}
  {\text{ }}2\mathop{\left){\vphantom{1{6{\text{ 25}}}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{6{\text{ 25}}}}}}
\limits^{\displaystyle \,\,\, 2} \\
  {\text{ - 4}} \\
  {\text{45 }}\left){\vphantom{1{2{\text{ 25}}}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{2{\text{ 25}}}}} \\
  {\text{ - }}\underline {{\text{2 25}}} \\
  {\text{ }}\underline {{\text{ 0 }}} {\text{ }} \\
\end{gathered} \]
Hence, the square root of 625 is 25.
Hence, the correct answer is the option (b).

Note:You can also recall that squares of numbers ending with digit 5 will also end with digit 5 and hence, conclude that the answer is the option (b).