Question

What is the square root 0f 10 times the square root of 20?

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 solution:
We have a square root of 10 times the square root of 20.
Square root of 10 means \[ \sqrt {10} \].
Square root of 20 means \[ \sqrt {20} \].
square root 0f 10 times the square root of 20.means \[ \sqrt {10} \times \sqrt {20} \].
Thus we have, \[ \sqrt {10} \times \sqrt {20} \]
Now we need to simplify this.
Now by suing product property of radicals we will have,
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = \sqrt {10 \times 20} \]
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = \sqrt {200} \]
We can write \[200 = 100 \times 2\]
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = \sqrt {100 \times 2} \]
We know that 100 is a perfect square and taking it outside we will have
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = 10\sqrt 2 \]
This is the exact form
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = 10 \times 1.414\].
\[ \Rightarrow \sqrt {10} \times \sqrt {20} = 14.14\] This is the decimal form.
So, the correct answer is “14.14”.

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 the 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.