Question

the order of the surd 7√8​

Answer 1

Answer:

Step-by-step explanation:

What is the order of SURD ∛ ∜ 8?

(iii) A surd with index of root 4 is called a fourth order surd. The surds which have the indices of four roots are called as forth order surds or bi-quadratic surds. For example ∜2, ∜4, ∜9, ∜20, ∜x are the surds of order 4.

Answer 2

SOLUTION

TO DETERMINE

The order of the surd

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

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

CONCEPT TO BE IMPLEMENTED

ORDER OF SURD

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

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

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

EVALUATION

1. Here the given number is

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

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

We get n = 2 & x = 392

Hence order of the surd = 2

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

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

We get n = 7 & x = 8

Hence order of the surd = 7

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