# CHECK IF THE RADICAL IS RATIONAL OR IRRATIONAL

Any number written with the radical sign  is called a radicand. An irrational radicand is called a surd.

To check if the radicand is rational or irrational ,we have to follow the steps.

Step 1 :

If the given number is prime, we can not do further simplification.

If the given number is composite number, we can decompose it as much as possible.

Step 2 :

In a square root, for every two same values multiplied, we can factor one out.

Step 3 :

If the given number can be written in the form with out square root, we can say it is perfect square, then it is rational.

If we have some thing still inside the square root, it is not perfect square, so it must be 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.

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