Quiz about Multiplying Radicals

Question 1

Simplify: $$\sqrt{15} \cdot \sqrt{15}$$ .

Accepted Answer

15

Answer

225

Answer

30

Answer

45

Question 2

Simplify: $$\sqrt[3]{16} \cdot \sqrt[3]{12}$$ .

Accepted Answer

$$4\sqrt[3]{3}$$

Answer

$$2\sqrt[3]{6}$$

Answer

$$\sqrt[3]{192}$$

Answer

8

Question 3

Simplify: $$2\sqrt{5m^3} \cdot \sqrt{5m}$$ .

Accepted Answer

$$10m^2\sqrt{m}$$

Answer

$$5m^2\sqrt{5m}$$

Answer

$$2m\sqrt{25m^4}$$

Answer

$$m\sqrt{10m^3}$$

Question 4

Simplify: $$-3\sqrt{15}(\sqrt{2} - 3\sqrt{3})$$ .

Accepted Answer

$$-3\sqrt{30} - 9\sqrt{135}$$

Answer

$$-3\sqrt{30} + 9\sqrt{45}$$

Answer

$$3\sqrt{30} - 9\sqrt{135}$$

Answer

$$-3\sqrt{30} + 9\sqrt{135}$$

Question 5

Simplify: $$\sqrt{3r}(3r + \sqrt{2})$$ .

Accepted Answer

$$3r\sqrt{3r} + \sqrt{6r}$$

Answer

$$3r^2 + 2$$

Answer

$$\sqrt{3r} + 3r\sqrt{2}$$

Answer

$$3r + \sqrt{2}$$

Question 6

Simplify: $$\sqrt{10}(4b + \sqrt{2})$$ .

Accepted Answer

$$4b\sqrt{10} + \sqrt{20}$$

Answer

$$4b\sqrt{10} + 2$$

Answer

$$$ 4b\sqrt{5} + \sqrt{5} $$$

Question 7

Simplify: $$(2 + \sqrt{2n})(-3 + \sqrt{2})$$ .

Accepted Answer

-6 + $$2\sqrt{2n}$$ - 3 $$\sqrt{2}$$ + $$\sqrt{4n}$$

Answer

-6 + $$\sqrt{2n}$$ - 3 $$\sqrt{2}$$ + 2 $$\sqrt{n}$$

Answer

-6 + $$\sqrt{2n}$$ - 3 $$\sqrt{2}$$ + $$\sqrt{2n}$$

Answer

-6 + $$2\sqrt{2n}$$ - 3 $$\sqrt{2}$$ + $$2\sqrt{n}$$

Question 8

Simplify: $$(-\sqrt{5b} - 4)(\sqrt{5} - 3)$$ .

Accepted Answer

-5\sqrt{5b} - 12\sqrt{5b} + 4\sqrt{5} - 12

Answer

-5 $$\sqrt{25b}$$ + 12 $$\sqrt{5b}$$ + 4 $$\sqrt{5}$$ - 12

Answer

-5\sqrt{5b} + 12\sqrt{5b} + 4\sqrt{5} - 12

Answer

-5 $$\sqrt{5b}$$ - 12 $$\sqrt{5b}$$ - 4 $$\sqrt{5}$$ - 12

Question 9

Simplify: $$\sqrt{8x^2} \cdot \sqrt{2x}$$ .

Accepted Answer

$$4x^2\sqrt{2}$$

Answer

$$4x\sqrt{2x}$$

Answer

$$2x\sqrt{16x^3}$$

Answer

$$2x^2\sqrt{2}$$

Question 10

Simplify: $$\sqrt{18}(5a + \sqrt{3})$$ .

Accepted Answer

$$5a\sqrt{18} + \sqrt{54}$$

Answer

$$5a\sqrt{9} + \sqrt{9}$$

Answer

$$5a\sqrt{18} + 3$$

Answer

$$5a\sqrt{18} + \sqrt{6}$$

Question 11

Simplify: $$(3 + \sqrt{3n})(-2 + \sqrt{3})$$ .

Accepted Answer

-6 + $$3\sqrt{3n}$$ - 2 $$\sqrt{3}$$ + $$\sqrt{9n}$$

Answer

-6 + $$\sqrt{3n}$$ - 2 $$\sqrt{3}$$ + $$\sqrt{3n}$$

Answer

-6 + $$\sqrt{3n}$$ - 2 $$\sqrt{3}$$ + 3 $$\sqrt{n}$$

Answer

-6 + $$3\sqrt{3n}$$ - 2 $$\sqrt{3}$$ + $$3\sqrt{n}$$

Multiplying Radicals

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