Question

Sum of squares of two numbers is 145. If the square root of one number is 3, find the square of the other number.

Answer 1

Hint: First we will assume two numbers to be x and y. We will form the equations using the given information and then substitute the values to get the values of x and y and then finally find the square of the one of the numbers.

Complete step by step answer:
Let the two numbers be x and y.
Now it is given that, the sum of squares of two numbers is 145
Hence,
\[{x^2} + {y^2} = 145\]………………. (1)
Also, it is given that squares root of one number is 3
Hence,
\[\sqrt x = 3\]
Squaring both the sides we get:-
\[\Rightarrow {\left( {\sqrt x } \right)^2} = {\left( 3 \right)^2}\]
Simplifying it further we get:-
\[\Rightarrow x = 9\]
Putting this value on equation 1 we get:-
\[\Rightarrow {9^2} + {y^2} = 145\]
Solving it further we get:-
\[\Rightarrow 81 + {y^2} = 145\]
Simplifying it further we get:-
\[\Rightarrow {y^2} = 145 - 81\]
\[\Rightarrow {y^2} = 64\]
Hence, the square of the other number is 64 and the number itself is:-
Taking square root of the above equation we get:-
\[\Rightarrow \sqrt {{y^2}} = \sqrt {64} \]
Simplifying it further we get:-
\[\Rightarrow y = \pm 8\]

$\therefore $ The square of the other number is 64. And the original numbers are 9, 8.

Note:
Students should note that when we take the square root of any number then we get two values both positive and negative values as the answer.
In such questions we have to use substitutions to get to the answer.