CHECK IF THE RADICAL IS RATIONAL OR IRRATIONAL

Tell whether each expression is rational or irrational.

Problem 1 :

-√64

Solution :

-√64

= -√(8 × 8)

= -8

-8/1 is in the form of a/b

So, -√64 is rational.

Problem 2 :

√1600

Solution :

√1600

1600 is in square root. 1600 is a whole number and also it is a perfect square.

So, we have

√1600 = √(40 × 40) = 40

So, √1600 is rational.

Problem 3 :

±√160

Solution :

±√160

The nearest perfect square of 160 is 169, means it is not a perfect square.

±√160 = 12.6491106…. (irrational)

12.6491106 …..  is a non terminating and non repeating decimal.

So, ±√160 is irrational number.

Problem 4 :

√144

Solution :

√144

144 is in square root. 144 is a whole number and also it is a perfect square.

So, we have

√144 = √(12 × 12) = 12

So, √144 is rational.

Problem 5 :

√125

Solution :

√125

√125 is an irrational, because 125 is not a perfect square.

√125 = 11.1803398….. (irrational)

11.1803398….. is a non terminating and non repeating decimal.

So, √125 is irrational number.

Problem 6 :

-√340

Solution :

-√340

-√340 is an irrational, because -340 is not a perfect square.

-√340 = 18.439088….. (irrational)

18.439088…..  is a non terminating and non repeating decimal.

So, -√340 is irrational number.

Problem 7 :

√1.96

Solution :

√1.96

1.96 is in square root. 1.96 is a decimal number and also it is a perfect square.

So, we have

√1.96 = √(1.4 × 1.4) = 1.4

So, √1.96 is rational.

Problem 8 :

-√0.09

Solution :

-√0.09

-√0.09 it can be expressed as a fraction in the form of -9/100.

-9/100

-9/100 is in the form of a/b

So, -√0.09 is a rational.