# Ex.6.1 Q1 Squares and Square Roots Solutions - NCERT Maths Class 8

## Question

What will be the unit digit of the squares of the following numbers?

(i) \(81\)

(ii) \(272\)

(iii) \(799\)

(iv) \(3853\)

(v) \(1234\)

(vi) \(26387\)

(vii) \(52698\)

(viii) \(99880\)

(ix) \(12796\)

(x) \(55555\)

## Text Solution

**What is known?**

Numbers

**What is unknown?**

Unit digit of the square of numbers

**Reasoning 1:**

If a number has \(1\) or \(9\) in its unit digit, then it’s square ends with \(1\).

\(\left( 1\times 1=1 \right)\)

**Steps:**

Since \(81\) has \(1\) as its unit digit, \(1\) will be the unit digit of its square.

**Similar Examples**

\(91, 721, 4321\)

**Reasoning 2:**

If a number has either \(2\) or \(8\) as its unit digit, then it’s square ends with \(4\).

**Steps:**

Since \(272\) has \(2\) as its unit digit, then its square number ends with \(4\).

\(\left( {2 \times 2 = 4} \right)\)

**Similar Examples**

\(22, 2432, 147322\)

**Reasoning 3:**

If a number has \(1\) or \(9\) in its unit digit, then it’s square ends with \(1\)

**Steps:**

Since \(799\) has \(9\) as its unit digit, \(1\) will be the unit digit of its square.

\(\left( 9\times 9=81 \right)\)

**Reasoning 4:**

If a number has either \(3\) or \(7\) as its unit digit, then its square number ends with \(9\).

**Steps:**

Since, \(3853\) has \(3\) as its unit digit, \(9\) will be the unit digit of its square.

\(\left( {3 \times 3 = 9} \right)\)

**Similar Examples**

\(13, 433, 63 \)

**Reasoning 5:**

If a number has either \(4\) or \(6\) as its unit digit, then its square ends with \(6\).

**Steps:**

Since, \(1234\) has \(4\) as its unit digit, \(6\) will be the unit digit of its square.

\(\left( {4 \times 4 = 16} \right)\)

**Similar Examples**

\(14, 114, 484, 1594\)

**Reasoning 6:**

If a number has either \(3\) or \(7\) as its unit digit, then its square number ends with \(9\).

**Steps:**

Since, \(26387\) has \(7\) as its unit digit, \(9\) will be the unit digit of its square.

\(\left( {7 \times 7 = 49} \right)\)

**Reasoning 7:**

If a number has either \(2\) or \(8\) as its unit digit, then it’s square ends with \(4\).

**Steps:**

Since \(52698\) has \(8\) as its unit digit, then its square number ends with \(4\).

\(\left( {8 \times 8 = 64} \right)\)

**Reasoning 8:**

If a number has \(0\) as its unit digit, then its square ends with \(0\).

**Steps:**

Since, \(99880\) has \(0\) as its unit digit, \(0\) will be the unit digit of its square.

**Similar Examples**

\(190, 1240, 167850\)

**Reasoning 9:**

If a number has either \(4\) or \(6\) as its unit digit, then its square ends with \(6\).

**Steps:**

Since, \(12796\) has \(6\) as its unit digit, \(6\) will be the unit digit of its square.

\(\left( {6 \times 6 = 36} \right)\)

**Reasoning 10:**

If a number has \(5\) as its unit digit, then its square ends with \(5\).

\(\left( 5\times 5=25 \right)\)

**Steps:**

Since, \(55555\) has \(5\) as its unit digit, \(5\) will be the unit digit of its square.

**Similar Examples**

\(105, 85, 3425\)