Question

write the simplest form of the rationalizing factor for the given surd 3√72 step by step explanation​

Answer 1

Answer:

∴ √2 is the simplest form of the rationalizing factor of 3√72. vi. 4√11 4√11 x √11 = 4 x 11 = 44, which is a rational number. ∴ √11 is the simplest form of the rationalizing factor of 4√11

hope it helps you....

Answer 2

Given,

The given number is = 3√72

To find,

The rationalising factor.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

According to the mathematical definition, if the product of two surds (or, irrational number) produces a rational number, then those surds (or, irrational number) will be rationalising factor of each other.

Now, the given number = 3√72

By simplifying the given number, we get :

= 3√72

= 3√(2×2×2×3×3)

= (3×2×3)×√2

= 18√2

Here, √2 is the surd which is needed to be rationalised. For that, we can multiply √2 by itself. (√2 is simplest possible choice here, for the rationalisation)

Because,

= √2 × √2

= 2

= Rational number

So,

= 18√2 × √2

= 18 × 2

= 36

= Rational number

Hence, √2 is the simplest form of rationalising factor.