Quizzes / CBSE / Class 8 / Mathematics / Squares and Square Roots

Estimating Square Roots Quiz - CBSE Class 8 Mathematics

Free practice quiz: Estimating Square Roots (CBSE Class 8 Mathematics). 11 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 11 multiple-choice questions on Estimating Square Roots, and 11 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 11 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

Trapping a root between integers

Find two perfect squares, one just below n and one just above n.
The square root of n lies between the square roots of those two perfect squares.

Bracketing rule

\[a^2 < n < (a+1)^2 \Rightarrow a < \sqrt{n} < a+1\]

Order is kept

\[0 \le p < q \Rightarrow \sqrt{p} < \sqrt{q}\]

Common mistake: Picking two integers whose squares do not actually lie on either side of n, or picking integers that are not consecutive.

Rounding to nearest whole number

Once a < √n < a+1, decide which integer √n is closer to.
Compare n with the square of the midpoint a + 1/2, not with the midpoint of the two squares.

Midpoint square

\[\left(a+\tfrac{1}{2}\right)^2 = a^2 + a + \tfrac{1}{4}\]

Round down

\[n < a^2 + a + \tfrac{1}{4} \Rightarrow \sqrt{n} \text{ rounds to } a\]

Round up

\[n > a^2 + a + \tfrac{1}{4} \Rightarrow \sqrt{n} \text{ rounds to } a+1\]

Common mistake: Assuming √n is nearer a just because n is nearer a² than (a+1)². Check against the midpoint square instead.

Refining to decimal places

Start from the whole-number estimate, then try decimals like a.d and square them.
Pick the decimals whose squares trap n, then round to the required decimal place.

Quick approximation

\[\sqrt{n} \approx a + \frac{n - a^2}{2a}\]

Squaring a trial decimal

\[(a + d)^2 = a^2 + 2ad + d^2\]

Common mistake: Stopping at the first trial decimal without squaring it to check whether it is too big or too small.

Square roots in real problems

The side of a square is the square root of its area.
Significant figures count from the first non-zero digit, so round the estimate there.

Side from area

\[s = \sqrt{A}\]

Product rule

\[\sqrt{k^2 m} = k\sqrt{m}\]

Common mistake: Dividing the area by the number of sides to find the side instead of taking the square root of the area.

Exam tips

Always check your estimate by squaring it and comparing with the original number.
Learn squares of integers up to at least twenty by heart for quick bracketing.
Read carefully whether the answer needs a whole number, decimal places or significant figures.

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

Which of the following is the closest estimate to √60?
Show answer
Answer: B. 7
7² = 49 and 8² = 64. Since 60 is closer to 49 than 64, √60 is closer to 7.
What is the approximate value of √300?
Show answer
Answer: B. 17
17² = 289 and 18² = 324. 300 is closer to 289 than 324.
Find an approximate value of √780, correct to one significant figure.
Show answer
Answer: C. 28
28² = 784 which is very close to 780. Therefore, the approximate value correct to one significant figure is 28.
Estimate the value of √1500 to the nearest whole number.
Show answer
Answer: B. 39
38² = 1444 and 39² = 1521. 1500 is closer to 1521 than 1444.
Estimate the square root of 2000.
Show answer
Answer: B. 45
44² = 1936 and 45² = 2025. 2000 is closer to 2025.

Take the full quiz

More quizzes

Browse all Squares and Square Roots quizzes

More to play

Daily ChallengeA new quiz every day. Keep your streak.HangmanGuess the word, letter by letter.Story QuestLearn through short interactive stories.All quizzesCBSE, ICSE, competitive exams and more.