Real Numbers : Test 2 - Class 10 MCQ

The prime factorization of 144 is as follows:

144 = 2 × 2 × 2 × 2 × 3 × 3

⇒ 144 = 24 × 32

We know that the exponent of a number am is m.

∴ The exponent of 2 in the prime factorization of 144 is 4.

If we multiply √3 we will get a perfect square 9 which is a rational number.

Use concept of HCF and LCM.

2 decimal places

We know that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
Here LCM = 36, HCF = 2 and b = 18
Then, 2 × 36 = a × 18
a = (2 × 36) / 18
a = 4
 

We know that LCM = Product of the greatest power of each prime factor, involved in the numbers. Since the power of 3 in LCM is 2, 

C = 3²× 5

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2n 5m, where n,

m are non-negative integers. Then x has a decimal expansion which terminates.

So 1/3 should be multiplied by 3/10 so that it is in the form of 2n5m.

When numbers are equal, LCM and HCF of two rational numbers are equal.