AI generatedNumberKey Stage 3

Estimating square roots

Estimating square roots.

  • Locate the number between two consecutive square numbers.
  • The root lies between their roots. Use the calculator value when rounding more precisely.

Example 1

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 2 and 3; nearest integer: 2.

Example 2

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 3 and 4; nearest integer: 3.

Your turn

Question 1

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Check answer
Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 4 and 5; nearest integer: 4.
Question 2

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Check answer
Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 5 and 6; nearest integer: 5.
Question 3

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Check answer
Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 6 and 7; nearest integer: 6.
Question 4

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Check answer
Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 7 and 8; nearest integer: 7.
Question 5

Between which two consecutive integers does this root lie? Give its value to the nearest integer.

Check answer
Find neighbouring perfect powers.The given number lies between these two powers.Use the calculator value to round to the nearest integer.
Between 8 and 9; nearest integer: 8.