How do you find the estimate for square roots?

Estimates for square roots can be found by identifying the position of numbers between consecutive square numbers.

How do you estimate calculations?

Round the numbers to an appropriate number of significant figures, then calculate with these numbers.

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Chapter Overview

Learning Goals

Maths

Estimation

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Summary

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Estimation

In a nutshell

Estimation means finding an approximate answer to a calculation. Estimating involves rounding numbers to $1$ or $2$ significant figures before performing a calculation. The estimated answer would be close to the actual answer.

Estimation in calculations

Round the numbers in the calculation to $1$ or $2$ significant figures before performing the calculation to find an approximate answer.

Example 1

Estimate the value of $\dfrac{67.9+2.16}{14.4}$ .

First, round all $3$ numbers to an appropriate number of significant figures:

$67.9 \mapsto 68$

$2.16 \mapsto 2$

$14.4 \mapsto 14$ 

Carry out the calculation with the rounded numbers:

$\dfrac{67.9+2.16}{14.4}\approx \dfrac{68+2}{14} = \dfrac{70}{14} = 5$

$\underline{\dfrac{67.9+2.16}{14.4} \approx 5}$

Estimation with square roots

Square roots can be estimated by identifying square numbers near a number.

Example 2

Estimate the value of $\sqrt{74}$ to $1\space d.p.$

$74$ is inbetween the square numbers $64$ and $81$ .

$\sqrt {64} = 8 \\\sqrt {81}= 9$ 

$74$ is closer to $81$ than $64$ .

Therefore, $\underline{\sqrt{74} \approx 8.7}$ 

Estimation

In a nutshell

Estimation in calculations

Round the numbers in the calculation to $1$ or $2$ significant figures before performing the calculation to find an approximate answer.

Example 1

Estimate the value of $\dfrac{67.9+2.16}{14.4}$ .

First, round all $3$ numbers to an appropriate number of significant figures:

$67.9 \mapsto 68$

$2.16 \mapsto 2$

$14.4 \mapsto 14$ 

Carry out the calculation with the rounded numbers:

$\dfrac{67.9+2.16}{14.4}\approx \dfrac{68+2}{14} = \dfrac{70}{14} = 5$

$\underline{\dfrac{67.9+2.16}{14.4} \approx 5}$

Estimation with square roots

Square roots can be estimated by identifying square numbers near a number.

Example 2

Estimate the value of $\sqrt{74}$ to $1\space d.p.$

$74$ is inbetween the square numbers $64$ and $81$ .

$\sqrt {64} = 8 \\\sqrt {81}= 9$ 

$74$ is closer to $81$ than $64$ .

Therefore, $\underline{\sqrt{74} \approx 8.7}$ 

Want to find out more? Check out these other lessons!

Rounding errors and estimating

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Frequently Asked Questions (FAQ)

FAQs

Question: What is estimation?

Answer: Estimation means finding an approximate answer to a calculation.
Question: How do you find the estimate for square roots?

Answer: Estimates for square roots can be found by identifying the position of numbers between consecutive square numbers.
Question: How do you estimate calculations?

Answer: Round the numbers to an appropriate number of significant figures, then calculate with these numbers.

Theory

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Estimation

Estimation

​​In a nutshell

Estimation in calculations

Example 1

Estimation with square roots

Example 2

Estimation

​​In a nutshell

Estimation in calculations

Example 1

Estimation with square roots

Example 2

Want to find out more? Check out these other lessons!

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In a nutshell

In a nutshell