Question

solve:
3√ 5 + √5 is equal to what?

Answer 1

3√ 5 + √5 is equal to 4√5.

Given :

3√ 5 + √5

To find :

The value of 3√ 5 + √5

Concept :

Like irrational numbers :

Irrational numbers having the same irrational factor are called similar or like irrational numbers.

For example:

√2, 8√2, 3√2, 5√2 are like rational numbers since all of these have the same irrational factor i e. √2

Additional of irrational numbers :

• Multiplication of irrational numbers is distributive over the addition of real numbers. So by this property Like irrational numbers can be added and subtracted.

• To add similar irrational numbers, add their coefficients.

• E.g 3√2 + 5√2 = √2(3 + 5) = 8√2

Solution :

Step 1:

Check whether the given number is like rational numbers or unlike.

Here, 3√ 5, and √5 are like rational numbers so they can be added.

Step 2 :

Add 3√ 5 + √5 by using distributive law:

3√ 5 + √5  = √5 (3 + 1)

3√ 5 + √5  = √5 (4)

3√ 5 + √5  = 4√5

Hence, 3√ 5 + √5 is equal to 4√5 .

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Answer 2

3√5 + √5 = 4√5

Given :

The expression 3√5 + √5

To find :

To simplify the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

3√5 + √5

Step 2 of 2 :

Simplify the given expression

Given two surds 3√5 and √5 are similar surds

Thus on addition we get

3√5 + √5

= (3 + 1)√5

= 4√5

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