Quiz about 9.4: Adding and Subtracting Radicals w/Multiplication

Question 1

When adding radicals, you must make sure the roots have the same __________ and the same ___________.

Accepted Answer

Index, Radicand

Answer

Radicand, Index

Answer

Index, Index

Answer

Radicand, Radicand

Question 2

Add the following radical expressions and simplify if possible.

$$4\sqrt[5]{7}+8\sqrt[5]{7}$$

Accepted Answer

$$12\sqrt[5]{7}$$

Answer

$$12\sqrt[10]{7}$$

Answer

Not Possible

Answer

$$12\sqrt[5]{14}$$

Question 3

Add the following radical expressions and simplify if possible.

$$3\sqrt[]{15}+\sqrt[]{15}$$

Accepted Answer

$$4\sqrt[]{15}$$

Answer

$$4\sqrt[4]{15}$$

Answer

Not Possible

Answer

$$4\sqrt[]{30}$$

Question 4

Add the following radical expressions and simplify if possible.

$$5\sqrt[7]{6}+5\sqrt[3]{6}$$

Accepted Answer

Not Possible

Answer

$$10\sqrt[4]{6}$$

Answer

$$7\sqrt[10]{6}$$

Answer

$$10\sqrt[5]{6}$$

Question 5

Add the following radical expressions and simplify if possible.

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

Accepted Answer

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

Answer

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

Answer

Not Possible

Answer

$$-2\sqrt[3]{24}$$

Question 6

Add the following radical expressions and simplify if possible.

$$\sqrt[4]{25}+\sqrt[4]{25}$$

Accepted Answer

$$2\sqrt[4]{25}$$

Answer

$$\sqrt[8]{25}$$

Answer

Not Possible

Answer

$$2\sqrt[8]{50}$$

Question 7

When subtracting radical expressions, make sure to subtract ____________ if the index and radicand are the same.

Accepted Answer

Coefficients

Answer

Index

Question 8

Subtract the following radical expressions and simplify if possible.

$$8\sqrt[4]{25}-3\sqrt[4]{25}$$

Accepted Answer

$$5\sqrt[4]{25}$$

Answer

$$5\sqrt[]{25}$$

Answer

Not Possible

Answer

$$5\sqrt[4]{0}$$

Question 9

Subtract the following radical expressions and simplify if possible.

$$11\sqrt[]{37}-\sqrt[]{37}$$

Accepted Answer

$$10\sqrt[]{37}$$

Answer

$$10\sqrt[]{0}$$

Answer

Not Possible

Answer

$$11\sqrt[]{37}$$

Question 10

Subtract the following radical expressions and simplify if possible.

$$8\sqrt[3]{22}-12\sqrt[3]{22}$$

Accepted Answer

$$-4\sqrt[3]{22}$$

Answer

$$4\sqrt[3]{22}$$

Answer

Not Possible

Answer

$$-4\sqrt[3]{0}$$

Question 11

Subtract the following radical expressions and simplify if possible.

$$-3\sqrt[]{42}-4\sqrt[]{42}$$

Accepted Answer

$$-7\sqrt[]{42}$$

Answer

$$\sqrt[]{42}$$

Answer

Not Possible

Answer

$$-\sqrt[]{42}$$

Question 12

Subtract the following radical expressions and simplify if possible.

$$15\sqrt[3]{21}-11\sqrt[]{21}$$

Accepted Answer

Not Possible

Answer

$$4\sqrt[]{21}$$

Answer

$$4\sqrt[1]{21}$$

Answer

$$4\sqrt[3]{21}$$

Question 13

When multiplying radical expressions, make sure to _____ coefficients.

Accepted Answer

Multiply

Answer

Add

Question 14

Multiply the following radical expressions, simplify if needed.

$$3\sqrt[]{5}\cdot4\sqrt[]{6}$$

Accepted Answer

$$12\sqrt[]{30}$$

Answer

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

Answer

$$12\sqrt[]{6}$$

Answer

$$12$$

Question 15

Multiply the following radical expressions, simplify if needed.

$$5\sqrt[]{8}\cdot4\sqrt[]{18}$$

Accepted Answer

$$240$$

Answer

$$20\sqrt[]{20}$$

Answer

$$20\sqrt[]{144}$$

Answer

$$9\sqrt[]{144}$$

Question 16

Multiply the following radical expressions, simplify if needed.

$$3\sqrt[3]{12}\cdot7\sqrt[3]{18}$$

Accepted Answer

$$126$$

Answer

$$6$$

Answer

$$21\sqrt[3]{196}$$

Answer

$$21\sqrt[3]{216}$$

9.4: Adding and Subtracting Radicals w/Multiplication

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