Question

Solve $ 5\sqrt 8 + 2\sqrt {32} - 2\sqrt 2 ?$

Answer 1

Hint: In this question, first we have to break the square root terms to their simplest form and then we have to use the basic algebraic calculation to get to the answer. In the end we can common out the root term from the equation.

Complete step-by-step answer:
In the given question, we have
$ \Rightarrow 5\sqrt 8 + 2\sqrt {32} - 2\sqrt 2 $
we need to break the square roots up into their simplest forms
 \[ \Rightarrow \,\sqrt 8 = \sqrt {4 \times 2} = \sqrt 4 \sqrt 2 = 2\sqrt 2 \]
$ \Rightarrow \sqrt {32} = \sqrt {8 \times 4} = \sqrt 4 \sqrt 4 \sqrt 2 = 4\sqrt 2 $
Now, put these values in the above equation:
$ \Rightarrow 5\left( {2\sqrt 2 } \right) + 2\left( {4\sqrt 2 } \right) - 2\sqrt 2 $
On multiplication, we get
$ \Rightarrow 10\sqrt 2 + 8\sqrt 2 - 2\sqrt 2 $
On doing addition in first two terms and the subtraction from the third term, we get
$ \Rightarrow 16\sqrt 2 $
Therefore, the value of $5\sqrt 8 + 2\sqrt {32} - 2\sqrt 2 $ is $16\sqrt 2 $.

Note: In this question there is only involvement of root two in the equation. But if there is involvement of some other number inside the root then there could be multiple terms in the answer. It is very convenient to find all the terms separately which involve square root or cube root and then use them in the equation at the time of calculation. In this question the root of any value is not specified. If this happens then take square root otherwise it would be specified that root of which value is using there.