Question

Estimate the value of the following to the nearest whole number :- 1) Square root of 80 2) Square root of 1000 3) Square root of 350 4) Square root of 500 explain in brief

Answer 1

Estimating Square Roots for a non perfect square can be done quickly if you know perfect squares.

1.√80= ?
64<80<81
8²<80<9²
8<√80<9

81-80= 1 & 80-64= 24
80 is more nearer to 81(=9²)
(Subtract from 9 in square root calculation)

81 - 80
= 1
(note difference to nearest known perfect square)

No. of Non perfect squares between 8² and 9²= 2*8
=16
{No. of Non perfect squares between successive squares a² and b²,(where b=a+1) =2*base of first no.
= 2a}

•°• √80= 9 - (1/16) = 9 - 0.0625= 8.9375(=~8.94)

2.√1000
= √(10²)
= (10)
{square and square root are inverse to each other,so gets cancelled}
or
by prime factorisation
1000= 2*2*2*2*5*5*5*5=2⁴*5⁴
√(1000)= (2⁴*5⁴)^(1/2)= 2*5= 10

3.√350= ?
324<350<361
18<√350<19

350-324=26 & 361-350= 11
350 is more nearer to 361(=19²)
(Subtract from 19 in square root calculation)

361-350= 11
(difference to nearest perfect square)

No. of non perfect square b/w 18² & 19²= 2*18
=36

•°•√350=19 - (11/36)= 19- 0.3055
=18.6945(=~ 18.70)

4. √500= ?
484<500<529
22<√500<23

500-484= 16 & 529-500= 29

500 is more nearer to 484(=22²)
(Subtract from 22 in square root calculation)

500-484= 16
(difference to nearest perfect square)

No. of non perfect square b/w 22² & 23²= 2*22
=44

•°•√500=22 + (16/44)= 22+ 0.3636
= 22.3636(=~22.36)

;)
hope it helps
comment if you need to clear something...

Answer 2

Answer:

Estimating Square Roots for a non perfect square can be done quickly if you know perfect squares.

1.√80= ?

64<80<81

8²<80<9²

8<√80<9

81-80= 1 & 80-64= 24

80 is more nearer to 81(=9²)

(Subtract from 9 in square root calculation)

81 - 80

= 1

(note difference to nearest known perfect square)

No. of Non perfect squares between 8² and 9²= 2*8

=16

{No. of Non perfect squares between successive squares a² and b²,(where b=a+1) =2*base of first no.

= 2a}

•°• √80= 9 - (1/16) = 9 - 0.0625= 8.9375(=~8.94)

2.√1000

= √(10²)

= (10)

{square and square root are inverse to each other,so gets cancelled}

or

by prime factorisation

1000= 2*2*2*2*5*5*5*5=2⁴*5⁴

√(1000)= (2⁴*5⁴)^(1/2)= 2*5= 10

3.√350= ?

324<350<361

18<√350<19

350-324=26 & 361-350= 11

350 is more nearer to 361(=19²)

(Subtract from 19 in square root calculation)

361-350= 11

(difference to nearest perfect square)

No. of non perfect square b/w 18² & 19²= 2*18

=36

•°•√350=19 - (11/36)= 19- 0.3055

=18.6945(=~ 18.70)

4. √500= ?

484<500<529

22<√500<23

500-484= 16 & 529-500= 29

500 is more nearer to 484(=22²)

(Subtract from 22 in square root calculation)

500-484= 16

(difference to nearest perfect square)

No. of non perfect square b/w 22² & 23²= 2*22

=44

•°•√500=22 + (16/44)= 22+ 0.3636

= 22.3636(=~22.36)

Step-by-step explanation: