Single Choice

Find the true statement for operations on surds

A$$a\sqrt{b}\pm c\sqrt{b}=(a\pm c)\sqrt{b}$$
Correct Answer
B$$\sqrt [ n ]{ a } \times \sqrt [ m ]{ y } =\sqrt [ mn ]{ ay } $$
C$$\sqrt [ n ]{ x } \div \sqrt [ m ]{ y } =\sqrt [ n ]{ x\div y } $$
D$$\sqrt [ n ]{ a } \pm \sqrt [ n ]{ b } =\sqrt [ n ]{ a\pm b } $$

Solution

a. $$a\sqrt{b} \pm c\sqrt{b} = (a\pm c)\sqrt{b}$$

b. $$\sqrt[n]{a} \times \sqrt[m]{y} \neq \sqrt[mn]{ay} $$ (As both bases are different)

c. $$\sqrt[n]{x} \div \sqrt[m]{y} = \dfrac{ \sqrt[n]{x}}{ \sqrt[m]{y}}$$

d. $$\sqrt[n]{a} \pm \sqrt[n]{a} \neq \sqrt[n]{a\pm b}$$

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

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:

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