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# How do you simplify $4$ square root $27$ $-$ square root $75?$

Last updated date: 20th Jul 2024
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Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example $5 \times 5 = 25$ , here the square root of $25$ is $5$ . There is no such formula to calculate square root formula but two ways are generally considered. They are the prime factorization method and division method. The symbol $\sqrt {}$ is used to denote square root and this symbol of square roots is also known as radical.

Here we have to find the value of $4\sqrt {27} - \sqrt {75}$ , since both are non perfect squares so we will factorise it under the root: $\sqrt {27}$ can be written as $9 \times 3$ and we know that $9$ is a perfect square and we can take out of the radical so we get,
$\sqrt {{3^2}} \times \sqrt 3$ $= 3\sqrt 3$ .
Similarly $\sqrt {75}$ can be further written as
$\sqrt {75} \Rightarrow {5^2} \times 3$ , It gives $\sqrt {{5^2}} .\sqrt 3 \Rightarrow 5\sqrt 3$ .
$4\sqrt {27} - \sqrt {75} = 4 \times 3\sqrt 3 - 5\sqrt 3$ .
On multiplying we have $12\sqrt 3 - 5\sqrt 3$ . It gives the value $7\sqrt 3$
Hence the answer is $7\sqrt 3 .$ .
So, the correct answer is “ $7\sqrt 3$ ”.