**Roots of integers worksheet :**

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

(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 = 8****²**

**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 = 8**³

**x**³** = 8**³

**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

**x**³** = (-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

x⁴ = (∜16)⁴

x⁴ = 16

**Step 3 :**

**Express 16 as the product of two same numbers**

**That is, 16 = 2 x 2 x 2 x 2**

**16 = 2**⁴

**x**⁴** = 2**⁴

**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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