Practice Questions for Algebra - Surds & Indices | CRE 2

1. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Find the rationalizing factor for 5 - 2√6.

(a)
5 - 2√6
(b)
- 5 - 2√6
(c)
5 + 2√6
(d)
None of these

2. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Rationalize $\frac{2}{\sqrt{5} - \sqrt{3}}$ .

(a)
(√5 + √3)/2
(b)
√5 + √3
(c)
√5 - √3
(d)
None of these

3. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Simplify $\frac{2}{\sqrt{3} - \sqrt{2}} - \frac{1}{3 - 2 \sqrt{2}}$ .

(a)
√3(√3 - 2)
(b)
√3(2 - √3)
(c)
2√3
(d)
None of these

4. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Find the square root of $[1 + \frac{1}{\sqrt{2} + \sqrt{1}} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \dots \dots \dots . \frac{1}{\sqrt{100} + \sqrt{99}}]$

(a)
(√3-1)/√2
(b)
2√2
(c)
2√3
(d)
√10

5. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Simplify: $\frac{a - b}{\sqrt[3]{a^{2}} + \sqrt[3]{ab} + \sqrt[3]{b^{2}}} - \frac{a + b}{\sqrt[3]{a^{2}} - \sqrt[3]{ab} + \sqrt[3]{b^{2}}}$

(a)
-2(ab)^1/3
(b)
a^1/3 - b^1/3
(c)
- 2b^1/3
(d)
(ab)^1/3

6. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Find the rationalizing factor of $2^{\frac{1}{3}} + 3^{\frac{1}{3}}$

(a) $2^{\frac{1}{3}} - 3^{\frac{1}{3}}$
(b)
$2^{\frac{1}{3}} + 3^{\frac{1}{3}}$
(c)
$(2^{2 / 3} + 6^{1 / 3} + 3^{2 / 3})$
(d)
$(2^{2 / 3} - 6^{1 / 3} + 3^{2 / 3})$

7. CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

Rationalise $\frac{4}{1 + \sqrt{2} + \sqrt{3}}$

(a)
√2 + √6 + 2
(b)
- √2 - √6 + 2
(c)
√2 - √6 + 2
(d)
√2 + √6 - 2

CRE 2 - Rationalization of Surds | Algebra - Surds & Indices

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