Question

How do you simplify square root 18 – square root 98?

Answer 1

Hint: Here we will first make the words problem convert into mathematical symbols. Then we will try to write or convert the problem in such a way that the root will have the same number so that we can perform the operation on the numbers outside the root.so let’s start.

Complete step-by-step answer:
Given that,
square root 18 – square root 98
this can be written as,
\[ = \sqrt {18} - \sqrt {98} \]
Now we can write the numbers in the root as,
\[ = \sqrt {9 \times 2} - \sqrt {49 \times 2} \]
Now 9 is the perfect square of 3 and 49 is the perfect square of 7. So we can write the simplified roots as,
\[ = 3\sqrt 2 - 7\sqrt 2 \]
Now we can subtract the numbers as,
\[ = - 4\sqrt 2 \]
If this option is not available we can write this in the form of power of 2.
 \[ = - {2^2}{2^{\dfrac{1}{2}}}\]
Now since the bases are same we can write them as, ……\[{a^m}{a^n} = {a^{m + n}}\]
\[ = - {2^{2 + \dfrac{1}{2}}}\]
On adding we get,
\[ = - {2^{\dfrac{5}{2}}}\]
This is also the correct answer.
So, the correct answer is “\[ - {2^{\dfrac{5}{2}}}\]”.

Note: Here the combination of algebraic mathematics and the rules of powers and indices can be combined. Also note that we took the number inside the root as in the form of product of 2 because the number remaining is the perfect square of a number that helps in subtracting the numbers.