Question

How do you simplify the square root of \[8\] + square root of \[32\] ?

Answer 1

Hint:In this question, we need to simplify and need to find the value of the square root of \[8\] + the square root of \[32\] . That is we need to find the sum of the square root of \[8\] and the square root of \[32\] . First, we should convert the two given radicals as radicals by using the square factors of the number, that is, we need to factorise both the given numbers in the square root since both are not perfect square numbers . After factoring the numbers, we can find the sum of the numbers.

Complete step by step solution:
Given square root of \[8\] + square root of \[32\] .
Here we need to find the sum of the square root of \[8\] and the square root of \[32\] .
Notation :
The square root of \[8\] ,
\[\Rightarrow \ \sqrt{8}\]
The square root of \[32\] ,
\[\Rightarrow \ \sqrt{32}\]
Here both \[\sqrt{8}\] and \[\sqrt{32}\] is not a perfect square. We need to factorise the given numbers to find the sum.
First let us factorise \[\sqrt{8}\] ,
\[\sqrt{8} = \sqrt{2 \times 2 \times 2}\]
\[\Rightarrow \ \sqrt{8} = \sqrt{2^{2} \times 2}\]
By taking the terms outside from the radical,
We get,
\[\sqrt{8} = 2\sqrt{2}\]
Now we need to factorise \[\sqrt{32}\] ,
\[\sqrt{32} = \sqrt{4 \times 4 \times 2}\]
\[\Rightarrow \ \sqrt{32} = \sqrt{4^{2} \times 2}\]
By taking the terms outside from the radical,
We get,
\[\sqrt{32} = 4\sqrt{2}\]
Now we can find the sum of \[\sqrt{8}\] and \[\sqrt{32}\] ,
\[\Rightarrow \ \sqrt{8} + \sqrt{32} = 2\sqrt{2} + 4\sqrt{2}\]
We know that \[a\sqrt{m} + b\sqrt{m} = \left( a + b \right)\sqrt{m}\]
Thus by adding
We get,
\[\sqrt{8} + \sqrt{32} = 6\sqrt{2}\]
Therefore the sum of the square root of \[8\] and the square root of \[32\] is \[6\sqrt{2}\]
The square root of \[8\] plus the square root of \[32\] is \[6\sqrt{2}\].

Note:
Square root of a number is a value in which it turns to the original number when it is multiplied by itself. Suppose \[x\] is a square root of \[y\] then it is represented as \[x = \sqrt{y}\] . For example, \[5\] is the square root of \[25\] then it is represented as \[5 = \sqrt{25}\] . Mathematically, the symbol \[\sqrt{}\] is known as the radical sign and known as the integral part of mathematics which is used to represent the square root. We need to know that to add and subtract radicals, they must be the same radical term. For the exponential numbers , we have a law of indices and by applying it we can easily solve the given number. We need to remember that when doing the addition or subtraction of exponential and radicand we have to make the like terms first.