Question

Find ‘x’ if
 $ x \times \dfrac{9}{{\sqrt 2 }} = 3\sqrt 2 $

Answer 1

Hint: We can find the value of x, by cross multiplying \[9/\sqrt{2}\]. When transferring \[9/\sqrt{2}\] to the other side, the numerator becomes the denominator and the denominator becomes the numerator. This reciprocal value is then multiplied by \[3\sqrt{2}\].

Complete step-by-step answer:
Given,
 $ x \times \dfrac{9}{{\sqrt 2 }} = 3\sqrt 2 $
From above we see that there is only one variable present in the given equation.
Shifting all other terms to the other side.
We have,
 $ x = 3\sqrt 2 \times \dfrac{{\sqrt 2 }}{9} $
We know that the product of two same irrational numbers gives out a rational number.
i.e. $ \sqrt a \times \sqrt a = a $
Using this in above problem and simplifying it. We have,
 $
  x = 3 \times \dfrac{2}{9} \\
   \Rightarrow x = \not \not 3{\,^1} \times \dfrac{2}{{\not 9{\,^3}}} \\
   \Rightarrow x = 1 \times \dfrac{2}{3} \\
   \Rightarrow x = \dfrac{2}{3} \;
  $
Therefore, from above we see that the value of ‘x’ is $ \dfrac{2}{3} $ .

Note: To solve any equation in algebra we first shift variables terms to one side and other terms to the other side. But if there are any multiple of divisible present with variable ‘x’ then shift them to the other side one by one using the basic rule of algebra to find the required value of ‘x’.