Question

How do you simplify the square root of 17 times the square root of 17 to the 2nd power?

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 17 times the square root of 17 to the 2nd power.
Square root of 17 means \[ \Rightarrow \sqrt {17} \].
Square root of 17 times the square root of 17 means \[ \Rightarrow \sqrt {17} \times \sqrt {17} \].
Square root of 17 times the square root of 17 to the 2nd power means
\[ \Rightarrow {\left( {\sqrt {17} \times \sqrt {17} } \right)^2}\]
Now we need to simplify this.
\[ \Rightarrow {\left( {{{\left( {\sqrt {17} } \right)}^2}} \right)^2}\]
We know that square and square root will cancel out.
\[ \Rightarrow {\left( {17} \right)^2}\]
\[ \Rightarrow 17 \times 17\]
\[ \Rightarrow 289\]. This is the required answer.

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 a ‘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.