Question

How do you simplify 5 times square root of 3 plus 4 times square root of 3?

Answer 1

We use the meaning of each word given in the expression and write the expression step-by-step according to the sequence of words given in the expression. Then taking common terms existing repeatedly, calculate the sum of terms.

• The word times means the number of times given number is multiplied i.e. ‘a’ times ‘b’ means $a \times b$.
• Square root means the number raised to the power half, which is represented by square root or under root of the number i.e. square root of ‘a’ means ${(a)^{1/2}} = \sqrt a$

Complete step-by-step answer:
We have to form an expression for the statement: 5 times square root of 3 plus 4 times square root of 3.
We use the meanings of the words ‘times’ and ‘square root’ to form the expression.
We have the square root of 3 in the statement i.e. we can write $\sqrt 3$
Now we have two elements in the statement i.e. “5 times square root of 3” and “4 times square root of 3”
We know the meaning of times is to multiply the number to the given number so, we can write
“5 times square root of 3” $= 5 \times \sqrt 3$ … (1)
And “4 times square root of 3” $= 4 \times \sqrt 3$ … (2)
Now we are given the statement as “5 times square root of 3 plus 4 times square root of 3”
So we add the two values obtained from equations (1) and (2)
$\Rightarrow$ “5 times square root of 3 plus 4 times square root of 3” will be $= 5 \times \sqrt 3 + 4 \times \sqrt 3$
Since $\sqrt 3$ exists in both terms, then we can take it common
$\Rightarrow$“5 times square root of 3 plus 4 times square root of 3” will be $= \sqrt 3 (5 + 4)$
$\Rightarrow$“5 times square root of 3 plus 4 times square root of 3” will be $= 9\sqrt 3$

$\therefore$ The value of “5 times square root of 3 plus 4 times square root of 3” is $9\sqrt 3$

Note:
Many students leave the answer after forming the equation only; keep in mind we have to simplify the equation i.e. we have to convert it into equation form and solve as much as possible.