ROOTS OF INTEGERS WORKSHEET

Roots of integers worksheet :

Here we are going to see some practice questions of the topic roots of integers.

Roots of integers worksheet - Practice questions

(1)  Find the real number root of √64

(2)  Find the real number root of ∛512

(3)  Find the real number root of ∛-8000

(4)  Find the real number root of ∜16

Question 1 :

Find the real number root of √64

Solution :

Step 1 :

Index of the given square root  =  2

Let "x" be the required root

x  =  √64

Step 2 :

In order to remove the square root, take squares on both sides

x²  =  (√64)²

x²  =  64

Step 3 :

Express 64 as the product of two same numbers

That is, 64 =  8 x 8

64  =  8²

x²  =  8²

Step 4 :

Since the powers are equal, then their base are also equal.

x  =  8

Hence the required root is 8.

Question 2 :

Find the real number root of ∛512

Solution :

Step 1 :

Index of the given square root  =  3

Let "x" be the required root

x  =  ∛512

Step 2 :

In order to remove the square root, raise power 3 on both sides

x³  =  (∛512)³

x³  =  512

Step 3 :

Express 512 as the product of two same numbers

That is, 512 =  8 x 8 x 8

512  =  8³

x³  =  8³

Step 4 :

Since the powers are equal, then their base are also equal.

x  =  8

Hence the required root is 8.

Question 3 :

Find the real number root of ∛-8000

Solution :

Step 1 :

Index of the given square root  =  3

Let "x" be the required root

x  =  ∛-8000

Step 2 :

In order to remove the square root, raise power 3 on both sides

x³  =  (∛-8000)³

x³  =  -8000

Step 3 :

Express -8000 as the product of two same numbers

That is, -8000 =  (-20) x (-20) x (-20)

-8000  =  (-20)³

x³  =  (-20)³

Step 4 :

Since the powers are equal, then their base are also equal.

x  =  -20

Hence the required root is -20.

Question 4 :

Find the real number root of ∜16

Solution :

Step 1 :

Index of the given square root  =  4

Let "x" be the required root

x  =  ∜16

Step 2 :

In order to remove the square root, raise power 3 on both sides

x  =  (∜16)

x  =  16

Step 3 :

Express 16 as the product of two same numbers

That is, 16 =  2 x 2 x 2 x 2

16  =  2

x  =  2

Step 4 :

Since the powers are equal, then their base are also equal.

x  =  2

Hence the required root is 2.

After having gone through the stuff given above, we hope that the students would have understood "Roots of integers worksheet".

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