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

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## 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

$$105, 85, 3425$$

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