Question

How do you simplify (Square root of 26) times (square root 2) + 4 (square root 13)?

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 (Square root of 26) times (square root 2) + 4 (square root 13)
Square root of 26 means \[ \Rightarrow \sqrt {26} \].
Square root of 2 means \[ \Rightarrow \sqrt 2 \].
Square root of 13 means \[ \Rightarrow \sqrt {13} \].
We know that if we have times we use multiplication operation then the given word problem becomes,
 \[ \Rightarrow \sqrt {26} \times \sqrt 2 + 4\sqrt {13} \]
We need to simplify this,
 \[ \Rightarrow \sqrt {26 \times 2} + 4\sqrt {13} \]
 \[ \Rightarrow \sqrt {52} + 4\sqrt {13} \]
Taking 4 inside the square root we will have
 \[ \Rightarrow \sqrt {52} + \sqrt {16 \times 13} \]
 \[ \Rightarrow \sqrt {52} + \sqrt {208} \]
 \[ \Rightarrow \sqrt {52} + \sqrt {52 \times 4} \]
Taking 4 outside we have,
 \[ \Rightarrow \sqrt {52} + 2\sqrt {52} \]
 \[ \Rightarrow 3\sqrt {52} \]. This is the exact form.
We know that \[\sqrt {52} = 7.21\]
 \[ \Rightarrow 3 \times 7.21\]
 \[ \Rightarrow 21.63\]. This is the decimal form.
So, the correct answer is “$3\sqrt {52}$”.

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.