Quiz about Simplifying Radicals with nth Roots

Question 1

$$2\sqrt{27}+8\sqrt{3}+5\sqrt{8}$$

Accepted Answer

$$14\sqrt{3}+10\sqrt{2}$$

Answer

$$24\sqrt{3}$$

Answer

$$24\sqrt{3}+5\sqrt{8}$$

Answer

$$14\ \sqrt[]{3}+3\ \sqrt[]{8}$$

Question 2

$$\sqrt[3]{16}-\sqrt[3]{250}$$

Accepted Answer

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

Answer

$$3\ \sqrt[]{-234}$$

Answer

$$7\sqrt[3]{2}$$

Answer

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

Question 3

$$5\sqrt{200}-5\sqrt{8}$$

Accepted Answer

$$40\sqrt{2}$$

Answer

$$60\sqrt{2}$$

Answer

$$\sqrt{8}$$

Answer

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

Question 4

Find the area of the rectangle

Accepted Answer

$$22\ +3\sqrt{6}$$

Answer

11

Answer

$$22+\sqrt{42}-2\sqrt{6}$$

Answer

$$34+11\sqrt{6}$$

Question 5

$$\left(3-4\sqrt{10}\right)\left(\sqrt{5}+2\sqrt{3}\right)$$

Accepted Answer

$$3\sqrt{5}+6\sqrt{3}-20\sqrt{2}-8\sqrt{30}$$

Answer

$$\sqrt{15}+18-4\sqrt{50}-8\sqrt{30}$$

Answer

$$-3\sqrt{88}$$

Answer

$$3\sqrt{5}+6\sqrt{3}-4\sqrt{50}-8\sqrt{30}$$

Question 6

$$3\sqrt{6}\left(\sqrt{6}-2\sqrt{10}\right)$$

Accepted Answer

$$18-12\sqrt{15}$$

Answer

$$6\sqrt{15}$$

Answer

$$-3\sqrt{24}$$

Answer

$$3\sqrt{36}-6\sqrt{60}$$

Question 7

$$3\sqrt[4]{96}-\sqrt[4]{486}-\sqrt[]{2}$$

Accepted Answer

$$3\sqrt[4]{6}-\sqrt[]{2}$$

Answer

$$3\ \sqrt[4]{6}-2\ \sqrt[]{2}$$

Answer

$$9\sqrt[4]{6}-3\ \sqrt[]{2}$$

Answer

$$3\sqrt[4]{6}-3\ \sqrt[]{2}$$

Question 8

$$3\ \sqrt[]{12}-\sqrt[]{12}+3\sqrt[3]{2}$$

Accepted Answer

$$4\ \sqrt[]{3}+3\sqrt[3]{2}$$

Answer

0

Answer

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

Answer

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

Question 9

$$\sqrt[]{15x}\left(5\ \sqrt[]{6}-5\ \sqrt[]{5x}\right)$$

Accepted Answer

$$15\ \sqrt[]{10x}-25x\ \sqrt[]{3}$$

Answer

$$-15x\ \sqrt[]{5x}+5$$

Answer

$$-8\ \sqrt[]{2x}+8x\ \sqrt[]{x}$$

Answer

$$10x\ \sqrt[]{3}-12x\ \sqrt[]{5x}$$

Question 10

$$2\sqrt[3]{-3}+3\ \sqrt[]{16}-2\sqrt[3]{81}$$

Accepted Answer

$$-8\sqrt[3]{3}+12$$

Answer

$$-14\sqrt[3]{3}+12$$

Answer

$$-14\sqrt[3]{3}$$

Answer

$$-14\sqrt[3]{3}+24$$

Question 11

$$\left(5\ \sqrt[]{3}+\ \sqrt[]{2}\right)\left(-\ \sqrt[]{3}-\ \sqrt[]{2}\right)$$

Accepted Answer

$$-17-6\ \sqrt[]{6}$$

Answer

$$-6+9\ \sqrt[]{6}$$

Answer

$$-10\ \sqrt[]{3}+5$$

Answer

$$-17$$

Question 12

$$\left(\sqrt[]{5}+\ \sqrt[]{2}\right)^2$$

Accepted Answer

$$7+2\ \sqrt[]{10}$$

Answer

$$7$$

Answer

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

Answer

$$5\ \sqrt[]{3}+2$$

Question 13

$$3\sqrt[3]{40}+3\sqrt[3]{40}$$

Accepted Answer

$$12\sqrt[3]{5}$$

Answer

$$24\sqrt[3]{5}$$

Answer

$$18\sqrt[3]{5}$$

Answer

$$6\sqrt[3]{5}$$

Question 14

$$2\ \sqrt[]{27}+2\ \sqrt[]{3}$$

Accepted Answer

$$8\ \sqrt[]{3}$$

Answer

$$0$$

Answer

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

Answer

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

Question 15

$$\sqrt[3]{-3a^7b^4}\cdot\sqrt[3]{36a^6b^2}$$

Accepted Answer

$$-3a^4b^2\sqrt[3]{4a}$$

Answer

$$\sqrt[3]{-108a^{13}b^8}$$

Answer

$$\sqrt[3]{-27a^{12}b^6}$$

Answer

$$-3a^{14}b^2\sqrt[3]{4b^2}$$

Simplifying Radicals with nth Roots

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