Question

the order of surd7√8​

Answer 1

Step-by-step explanation:

TO DETERMINE

The order of the surd

1. \: \: \: 7 \sqrt{8}1.7

8

2. \: \: \sqrt[7]{8}2.

7

8

CONCEPT TO BE IMPLEMENTED

ORDER OF SURD

If an irrational numbers can be written in the form \sf{ \sqrt[n]{x} }

n

x

Where x is a rational number and n is a natural number

\sf{Then \: \: n \: \: is \: the \: order \: of \: the \: surd \: \: \sqrt[n]{x} }Thennistheorderofthesurd

n

x

EVALUATION

1. Here the given number is

7 \sqrt{8} = \sqrt{392} = \sqrt[2]{392}7

8

=

392

=

2

392

Comparing with \sf{ \sqrt[n]{x} }

n

x

We get n = 2 & x = 392

Hence order of the surd = 2

2. Here the given number is \sqrt[7]{8}

7

8

Comparing with \sf{ \sqrt[n]{x} }

n

x

We get n = 7 & x = 8

Hence order of the surd = 7