problem solving surds questions

Surds Questions

Surds questions are given in this article for students with complete explanations. Here, we have provided a number of surds questions, which will help them understand the concept easily. The most important topic covered in primary and secondary schools is surds. Hence, practise the surds questions below and cross-verify your answers with the explanation provided. To learn more about surds, click here .

Surds Questions with Solutions

Go through the below surds problems and practise them as well.

1. Determine the product of 2√3 and 3√5.

Given surds are 2√3 and 3√5.

Thus, 2√3 × 3√5 = 2 × 3 × √3 × √5

2√3 × 3√5 = 6 × √(3 × 5)

2√3 × 3√5 = 6 × √15.

Therefore, the product of 2√3 and 3√5 is 6√15.

2. How to write the surd √7 in an exponential form?

Given surd: √7.

We know that we can write the surds in exponential form:

i.e., √a = a 1/2 .

Similarly, √7 can be written as 7 1/2 .

Therefore, √7 in exponential form is 7 1/2 .

3. Simplify the surd √18.

Given surd: √18.

√18 is simplified as follows:

We know that 18 can be written as 3 × 3 × 2.

√18 = √(3 × 3 × 2)

√18 = √3 × √3 ×√2

√18 = (√3) 2 ×√2

Now, cancel out square and square root on the right-hand side, and we get

Hence, the simplified form of surd √18 is 3√2.

4. Can we add similar surds?

Yes, we can add similar surds. We know that if the surds contain the same irrational factors, we can say that the surd is a similar surd.

For example, we can add 4√2 and 2√2.

Because, in both the surds, √2 is an irrational number .

Thus, we get

4√2 + 2√2 = 6√2.

5. Simplify the surd: 2√3 + 7√3.

Given: 2√3 + 7√3

As we know, the surds cannot be added. But, we can add similar surds:

Hence, 2√3 + 7√3 = (2 + 7)√3

2√3 + 7√3 = 9√3.

Hence, the simplified form of the surd 2√3 + 7√3 is 9√3

6. Write the surd 4 / (1 + 2√3) in the simplest form:

To simplify the given surd expression, change the sign in the denominator of the surd expression and simplify it.

Hence, the simplification of the given surd is:

7. Simplify the surd: √21 × √15.

Given: √21 × √15

We know that 21 can be written as 7 × 3

Similarly, 15 can be written as 3 × 5

Hence, √21 × √15 = √(7 × 3) × √(3 × 5)

√21 × √15 = √(7 × 3 × 3 × 5)

√21 × √15 = 3 √(7×5)

√21 × √15 = 3√35

Hence, the simplification of the surd √21 × √15 is 3√35.

8. Write the surd expression in exponential form: ∜6 + √10.

Given surd expression: ∜6 + √10

The exponential form of the given surd expression is:

∜6 + √10 = 6 1/4 + 10 1/2 .

9. Determine the order of the surd ∛11.

Given surd: ∛11

In the surd ∛11, the index is 3.

The surd ∛11 is read as the cube root of 11.

Hence, the order or the index of the given surd is 3.

10. Subtract the surd 12√45 from the surd 25√20.

To find: 25√20 – 12√45.

Now, simplify the given surds into its simplest form.

Thus, 25√20 – 12√45 = 25√(2 × 2 × 5) – 12√(3 × 3 × 5)

25√20 – 12√45 = 25×2 √5 – 12×3 √5.

25√20 – 12√45 = 50√5 – 36√5

Now, we can subtract the similar surds.

Hence, 25√20 – 12√45 = 14√5.

Explore More Articles:

• Polynomials Questions
• Lines and Angles Questions
• Cube Root Questions
• Prime Numbers Questions
• Compound Interest Questions

Practice Questions

Answer the following questions:

• Find the order of the surd 7∜3.
• \(\begin{array}{l}\text{Simplify the surd:  }\frac{7}{\sqrt{5}-\sqrt{11}}\end{array} \)
• Add the surd: 7√10 + 11√10.

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