Question

How do you simplify $\sqrt {81{x^4}} $?

Answer 1

Hint:In order to write the expression into the simplest form, factorize the base part of the value inside the square root such that it contains perfect squares in it. Since in our case we have the largest factor as 81 who is a perfect square ,we'll use here the prime factorisation of 81 and pull out terms from the inside of the square root.
Formula:
${(a)^{\dfrac{m}{n}}}$=${({a^m})^{\dfrac{1}{n}}}$
${x^{m + n}} = {x^m} \times {x^n}$

Complete step by step solution:
Given a expression
$\sqrt {81{x^4}} $
First Separating the value $81$ into its factors, So the factors of $81$ comes to be,
$1,3,9,27,81$
Now let’s find the factors who are perfect squares of some number, we got
$1,9$
Let’s consider the largest perfect square form the factors of 81 and divide it with 81 ,we get
$
= \dfrac{{81}}{9} \\
= 9 \\
$
From the above we can say that $81 = 9 \times 9$
Replace $81$as $9 \times 9$ in the original number and ${x^4}\,as\,{({x^2})^2}$
$ = \sqrt {{{\left( {9{x^2}} \right)}^2}} $
Taking out $\left( {9{x^2}} \right)$ from inside the square root.
$ = 9{x^2}$
Therefore, $\sqrt {81{x^4}} $ in the simplest form $9{x^2}$

Additional Information:
1. If you want to Increase a Number by y %:
Example:
On the off chance that a number is expanded by \[10{\text{ }}\% \], at that point it becomes 1.1 times of itself.
On the off chance that a number is expanded by 30 %, at that point it becomes 1.3 times of itself.
2. If you want to Decrease a Number by y %:
Example:
On the off chance that a number is diminished by 10 %, at that point it becomes 0.90 times of itself.
On the off chance that a number is diminished by 30 %, at that point it becomes 0.70 times of itself.

Note:
1. Don’t Forgot to cross check the answer.
2. To calculate fraction from the percentage, divide the given percentage value by 100
For example: We have to write $70\% $ into fraction
$
= \dfrac{{70}}{{100}} \\
= \dfrac{7}{{10}} \\
$
Or
$ = 0.7$
3.Numbers apart from perfect squares are imperfect squares.