Name: Method of Estimating the Square Roots of Numbers
Uploaded: 2019-07-19
Duration: 6 min 15 s
Description: How to figure out the nearest square root of a non-perfect square number or guessing the square root of a perfect square number? Let's learn in this video.

Question

Let's find the similarity between the digits in the units place of an integer and square number.

	Integer	Square Number $(a \times a)$	Unit place of square number
$0$ in units	$10, 20, 30 . . .$	$100, 400, 900 . . .$	Unit place of square _____
$1$ in units	$11, 21, 31 . . .$	$121, 441, 961 . . .$	Unit place of square $1$
$2$ in units	$12, 22, 42 . . .$	$144,$ _____ $,$ _____	Unit place of square _____
$3$ in units	$13, 23, 53 . . .$	$169,$ _____ $,$ _____	Unit place of square _____
$4$ in units	$14, 24, 44 . . .$	$196,$ _____ $, 1936 . . .$	Unit place of square _____
$5$ in units	$15, 25, 35 . . .$	$225,$ _____ $,$ _____	Unit place of square _____
$6$ in units	$16, 26, 66 . . .$	$256,$ _____ $,$ _____	Unit place of square _____
$7$ in units	$17, 27, 57 . . .$	$289,$ _____ $,$ _____	Unit place of square _____
$8$ in units	$18, 28, 78 . . .$	$324,$ _____ $,$ _____	Unit place of square _____
$9$ in units	$19, 29, 39 . . .$	$361,$ _____ $,$ _____	Unit place of square _____

Accepted Answer

The given table is as follows,

Integer Square Number $(a \times a)$ Unit place of square number

$0$ in units $10, 20, 30 . . .$ $100, 400, 900 . . .$ Unit place of square _____

$1$ in units $11, 21, 31 . . .$ $121, 441, 961 . . .$ Unit place of square $1$

$2$ in units $12, 22, 42 . . .$ $144,$ _____ $,$ _____ Unit place of square _____

$3$ in units $13, 23, 53 . . .$ $169,$ _____ $,$ _____ Unit place of square _____

$4$ in units $14, 24, 44 . . .$ $196,$ _____ $, 1936 . . .$ Unit place of square _____

$5$ in units $15, 25, 35 . . .$ $225,$ _____ $,$ _____ Unit place of square _____

$6$ in units $16, 26, 66 . . .$ $256,$ _____ $,$ _____ Unit place of square _____

$7$ in units $17, 27, 57 . . .$ $289,$ _____ $,$ _____ Unit place of square _____

$8$ in units $18, 28, 78 . . .$ $324,$ _____ $,$ _____ Unit place of square _____

$9$ in units $19, 29, 39 . . .$ $361,$ _____ $,$ _____ Unit place of square _____

We know that, a square number or perfect square is an integer that is the square of an integer.

So, now lets find the squares of the given numbers and then observe their unit's digit.

Integer Square Number $(a \times a)$ Unit place of square number

$0$ in units $10, 20, 30 . . .$ $100, 400, 900 . . .$ Unit place of square $0$

$1$ in units $11, 21, 31 . . .$ $121, 441, 961 . . .$ Unit place of square $1$

$2$ in units $12, 22, 42 . . .$ $144, 484, 1764 . . .$ Unit place of square $4$

$3$ in units $13, 23, 53 . . .$ $169, 529, 2809 . . .$ Unit place of square $9$

$4$ in units $14, 24, 44 . . .$ $196, 576$ $, 1936 . . .$ Unit place of square $6$

$5$ in units $15, 25, 35 . . .$ $225, 625, 1225 . . .$ Unit place of square $5$

$6$ in units $16, 26, 66 . . .$ $256, 676, 4356 . . .$ Unit place of square $6$

$7$ in units $17, 27, 57 . . .$ $289, 729, 3249 . . .$ Unit place of square $9$

$8$ in units $18, 28, 78 . . .$ $324, 784, 6084 . . .$ Unit place of square $4$

$9$ in units $19, 29, 39 . . .$ $361, 841, 1521 . . .$ Unit place of square $1$

We observe, the square numbers which has $0$ in unit's place, their square value also has $0$ in units.

The square numbers which has $4$ in unit's place, their square value has $6$ in units.

The square numbers which has $5$ in unit's place, their square value has $5$ in units.

The square numbers which has $6$ in unit's place, their square value has $6$ in units.

The square numbers which has $9$ in unit's place, their square value has $1$ in units.

West Bengal Board Solutions for Chapter: Square Root, Exercise 11: Exercise 11

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Square Root, Exercise 11: Exercise 11

Questions from West Bengal Board Solutions for Chapter: Square Root, Exercise 11: Exercise 11 with Hints & Solutions

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