Single Choice

Express as a pure surd: $$a \sqrt [ 3 ]{ { b }^{ 2 } } $$

A$$\sqrt [ 3 ]{ { a }^{ 3 }{ b }^{ 2 } } $$
Correct Answer
B$$\sqrt [ 3 ]{ { a }^{ 2 }{ b }^{ 3 } } $$
C$$\sqrt [ 2 ]{ { a }^{ 3 }{ b }^{ 2 } } $$
D$$\sqrt [ 2 ]{ { a }^{ 2 }{ b }^{ 3 } } $$

Solution

A surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd.

$$a\sqrt[3]{b^2} = \sqrt[3]{a^3}\times \sqrt[3]{b^2} = \sqrt[3]{a^3b^2}$$

SIMILAR QUESTIONS

Exponents and Powers

Express as a pure surd: $$x\sqrt{x+y}$$

Exponents and Powers

Express as a pure surd: $$2\sqrt [ 3 ]{ 4 } $$

Exponents and Powers

Express as a pure surd: $$3\sqrt [ 4 ]{ 5 }$$

Exponents and Powers

Express as a mixed surd: $$\sqrt{80}$$

Exponents and Powers

Express as a mixed surd: $$\sqrt [ 3 ]{ 256} $$

Exponents and Powers

Express as a mixed surd: $$\sqrt [ 4 ]{ 1280 } $$

Exponents and Powers

Express as a mixed surd: $$\sqrt [ 5 ]{ 320 } $$

Exponents and Powers

$$\sqrt{12\sqrt{5}+2\sqrt{55}}=$$...........

Exponents and Powers

If $$x=\sqrt [ 3 ]{ 9 } ,y=\sqrt [ 4 ]{ 11 } ,z=\sqrt [ 6 ]{ 17 } $$ then:

Exponents and Powers

Find the true statement for operations on surds

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