Tag: estimating square roots

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Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square Also find the square root of the perfect square so obtained 
$(i) 402, (ii) 1989, (iii) 3250, (iv) 825, (v) 4000$

  1. <span class="block ng-binding">Least number which must be subtracted:$(i) 2, (ii) 22, (iii) 1, (iv) 21, (v) 52$

    Square root of the perfect square:
    $(i) 20, (ii) 34 ,(iii) 55, (iv) 26, (v) 67$
  2. <span class="block ng-binding">Least number which must be subtracted:$(i) 2, (ii) 53, (iii) 1, (iv) 41, (v) 31$

    Square root of the perfect square:
    $(i) 20, (ii) 44, (iii) 57, (iv) 28, (v) 63$
  3. <span class="block ng-binding">Least number which must be subtracted:$(i) 6, (ii) 22, (iii) 50, (iv) 31, (v) 40$

    Square root of the perfect square:
    $(i) 19, (ii) 41, (iii) 49 ,(iv) 27 ,(v) 65$
  4. <span class="block ng-binding">Least number which must be subtracted:$(i) 8, (ii) 41, (iii) 12, (iv) 56, (v) 4$

    Square root of the perfect square:
    $(i) 19 ,(ii) 22, (iii) 37, (iv) 26, (v) 61$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For $402$

Nearest perfect square is $400$
$\sqrt{400}$ $=$ $20$
$402$ $-$ $400$ $=$ $2$
For $1989$
Nearest perfect square is $1936$

$\sqrt{1936}$ $=$ $44$
$1936$ $-$ $1989$ $=$ $53$

For $3250$
Nearest perfect square is $3249$

$\sqrt{3249}$ $=$ $57$
$3250$ $-$ $3249$ $=$ $1$
For $825$
Nearest perfect square is $784$
$\sqrt{784}$ $=$ $28$
$825$ $-$ $784$ $=$ $41$
For $4000$
Nearest perfect square is $3969$
$\sqrt{3969}$ $=$ $63$
$4000$ $-$ $3969$ $=$ $31$
From this, Option B is correct answer.

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Mr. Hansraj wants to find the least number of boxes to be added to get a perfect square. He already has $7924$ boxes with him. How many more boxes are required?

  1. $819$
  2. $412$
  3. $419$
  4. $176$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Find square root by long division method.

$\therefore \sqrt {7924}$ = $89.01$

Hence, the perfect square number smaller than $7924$ is
$89^2 = 7921$
The next perfect square no. is $90^2 = 8100$

So, $8100 - 7924 = 176$
Therefore, the man needs $176$ more boxes in order to get a perfect square number.
So, option D is correct.

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

Estiamate the square root of $850$ 

  1. $29.15$
  2. $30.21$
  3. $98.23$
  4. $23.11$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of $850$ is $\sqrt {850}=\sqrt {25 \times 34}=5\sqrt {34}$

Square root of $34$ lie between $5$ and $6$.
 square of $5.5$ is $30.25$ 
Now, we can say that square root of $34$ lie between $5.5$ and $6$.
Now, square of $5.75$ is $33.06$
So, square root of $34$ lie between $5.75$ and $6$.
Now, we have to choose the number $5.85$
$(5.85)^2=34.225$ which is greater than $34$ and close to $34$
So, assume a number $5.84$.
$(5.84)^2=34.1056$
$(5.83)^2=33.9889$
Hence, we can say that square root of 34 lie between $5.83$ and $5.84$.
So, $5\times 5.83=29.15$.