# nth Root of a

We will discuss here about the meaning of $$\sqrt[n]{a}$$.

The expression $$\sqrt[n]{a}$$ means ‘nth rrot of a’. So, ($$\sqrt[n]{a}$$)^n = a.

Also, (a1/a)n = a n × 1/n = a1 = a.

So, $$\sqrt[n]{a}$$ = a1/n.

Examples:

1. $$\sqrt[3]{8}$$ = 81/3

= (23)1/3

= 23 × 1/3

= 21

= 2.

2. $$\sqrt[4]{9}$$ = 91/4

= (32)¼

= 32 × ¼

= 31/2

= √3.

Note: 31/2 = $$\sqrt[2]{3}$$. But $$\sqrt[2]{3}$$ is also written as √3.

Solved examples on nth Root of a:

Express each of the following in the simplest form without radicals:

(i) $$\sqrt[4]{5^{2}}$$

(ii) $$\sqrt[n]{x^{m}}$$

(iii) $$\sqrt[3]{64^{-4}}$$

Solution:

(i) $$\sqrt[4]{5^{2}}$$ = (52)1/4

= 52 × 1/4

(ii) $$\sqrt[n]{x^{m}}$$ = (xm)1/n

= xm × 1/n

= xm/n.

(iii) $$\sqrt[3]{64^{-4}}$$ = (64-4)1/3

= 64-4 × 1/3

= 64-4/3

= (43)-4/3

= 43(-4/3)

= 4-4

= $$\frac{1}{4 × 4 × 4 × 4}$$

= $$\frac{1}{256}$$.

From nth Root of a to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

## Recent Articles

1. ### Expanded form of Decimal Fractions |How to Write a Decimal in Expanded

Jul 22, 24 03:27 PM

Decimal numbers can be expressed in expanded form using the place-value chart. In expanded form of decimal fractions we will learn how to read and write the decimal numbers. Note: When a decimal is mi…

2. ### Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

Jul 22, 24 02:41 PM

Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

3. ### Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

Jul 21, 24 02:14 PM

Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

4. ### Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

Jul 20, 24 03:45 PM

When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…