Question

What is the square root of 5 times the square root of 10?

Answer 1

Hint: First we need to convert the given word problem into algebraic expression. That is an algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. After obtaining the algebraic expression we can simplify.

Complete step-by-step answer:
We have a square root of 5 times the square root of 10.
Now the square root of 10 means \[ \Rightarrow \sqrt {10} \].
Now the square root of 5 means \[ \Rightarrow \sqrt 5 \].
Now square root of 5 times the square root of 10 means
\[ \Rightarrow \sqrt 5 \times \sqrt {10} \]. This is the required result.
We can simplify it further.
\[ \Rightarrow \sqrt {5 \times 10} \]
\[ \Rightarrow \sqrt {50} \]
\[ \Rightarrow \sqrt {25 \times 2} \]
\[ \Rightarrow 5\sqrt 2 \]. This is the simplified form.
So, the correct answer is “\[ \Rightarrow 5\sqrt 2 \]”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation\[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have ‘quotient’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.