Question

How do you simplify \[3 \times \] square root of 20 divided by square root of 36?

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 \[3 \times \] square root of 20 divided by square root of 36.
Square root of 20 means \[ \Rightarrow \sqrt {20} \].
\[3 \times \] square root of 20 means \[ \Rightarrow 3 \times \sqrt {20} \].
Now square root of 36 means \[ \Rightarrow \sqrt {36} \]
Then \[3 \times \] square root of 20 divided by square root of 36 means
\[ \Rightarrow \dfrac{{3 \times \sqrt {20} }}{{\sqrt {36} }}\]
Now we need to simplify this.
We know that 36 is a perfect square.
\[ \Rightarrow \dfrac{{3 \times \sqrt {20} }}{6}\]
Cancelling we have,
\[ \Rightarrow \dfrac{{\sqrt {20} }}{2}\]
\[ \Rightarrow \dfrac{{\sqrt {4 \times 5} }}{2}\]
We know 4 is a perfect square,
\[ \Rightarrow \dfrac{{2\sqrt 5 }}{2}\]
\[ \Rightarrow \sqrt 5 \]. This is the exact form.
\[ \Rightarrow 2.24\]. This is the decimal form.

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.