Mathematics 0580 · IGCSE
Powers and roots
89 practice questions on Powers and roots, with worked solutions and instant marking.
Find $\sqrt{196}$.
Feb/March 2017
Determine the value of $(\sqrt{25})^2$.
Feb/March 2018
Calculate $\sqrt[3]{-4.3 \times 6.7^2}$ and record all the figures displayed by your calculator.
Feb/March 2018
Calculate the value of $\sqrt{17.8} - 1.3^{2.5}$.
Feb/March 2018
Write down the reciprocal for 40.
Feb/March 2020
Calculate the numerical value of $\sqrt{7.29}$.
Feb/March 2021
Simplify the expression $(3125w^{3125})^{\frac{1}{5}}$.
Feb/March 2023
Calculate $\sqrt{5.76} + 2.8^3$.
Feb/March 2024
Calculate the value of $\sqrt{5.76} + 2.8^3$.
Feb/March 2024
Find $10^3$.
Feb/March 2025
Calculate $\dfrac{20.24 - \sqrt[3]{30}}{6.5}$. State your answer correct to 1 decimal place.
Feb/March 2025
With a calculator, find $\sqrt{4.2^2 + 5.8^2}$.
May/June 2015
Use a calculator to determine $\sqrt{10 + 0.6 \times (8.3^2 + 5)}$.
May/June 2015
Find the value of $(\frac{1}{4})^{0.5}$.
May/June 2015
Determine the cube root of $4913$.
May/June 2016
Determine the simplified form of $(16p^{16})^{\frac{1}{4}}$.
May/June 2016
The numbers in the list are 8, 9, 10, 11, 12, 13, 14, 15 and 16.
May/June 2016
Determine the cube root of 4913.
May/June 2016
Five number cards are shown: 1, 2, 6, 7 and 8.
May/June 2016
Calculate $\dfrac{\sqrt[3]{512}}{6^2}$. Give the answer as a fraction in lowest terms.
May/June 2017
Calculate the value of $\sqrt{120} + 3.8^2 - 25$.
May/June 2017
Find the value of $17^3$.
May/June 2017
Calculate $125^{\frac{2}{3}}$.
May/June 2017
Calculate $\sqrt{120} + 3.8^2 - 25$.
May/June 2017
Simplify the expression $\left(\frac{8}{a^{12}}\right)^{\frac{1}{3}}$.
May/June 2017
Calculate $\sqrt{2.38 + 6.4^2}$ and record the full calculator display.
May/June 2018
Calculate $sqrt{dfrac{18^2}{0.5 + 1.75}}$.
May/June 2018
Find the exact value for $8^{\frac{2}{3}} \times 49^{-\frac{1}{2}}$.
May/June 2018
Determine the value of $\left(\frac{1}{81}\right)^{-\frac{3}{4}}$.
May/June 2018
Find the value of $\sqrt{19044}$.
May/June 2018
Calculate the value of $-12 \div -2$.
May/June 2019
Calculate $\sqrt[3]{8.1^2 - 1.3^{0.8}}$.
May/June 2019
Calculate the value.
May/June 2019
The solids listed below each have a volume of $1000\,\text{cm}^3$.
May/June 2019
Calculate $\sqrt[4]{0.0256}$.
May/June 2021
Calculate the value of $\sqrt[4]{0.0256}$.
May/June 2021
Find the numerical value of $\sqrt{68} \times \sqrt{153}$.
May/June 2022
Find the radius of a hemisphere whose volume is $80\text{ cm}^3$. [The volume, $V$, of a sphere with radius $r$ is $V = \dfrac{4}{3}\pi r^3$]
May/June 2022
Calculate the value of $4^5 - 5^4$.
May/June 2022
Find the value of $\frac{m k^3}{\sqrt{3}}$ when $m = 4$ and $k = 7$.
May/June 2022
Calculate the value of $\sqrt{42} + 3^{0.4}$.
May/June 2023
Calculate the value of $\sqrt[3]{343} - \sqrt{40.96}$.
May/June 2024
Calculate the value of $\sqrt[3]{343} - \sqrt{40.96}$.
May/June 2024
State the value of $\sqrt{36}$.
May/June 2025
State the value of $\sqrt{169}$.
May/June 2025
Determine the value of $\sqrt{1.96}$.
May/June 2025
Calculate $\dfrac{2.8^5 - 0.3^2}{\sqrt{5}}$. Round your answer to 2 decimal places.
May/June 2025
Find the value of the following:
Oct/Nov 2015
Solve for $x$ in $29 - x = 18$.
Oct/Nov 2015
Simplify $\sqrt{36x^{16}}$.
Oct/Nov 2016
Arrange these from smallest to largest: $0.6^3$, $0.22$, $\sqrt{0.09}$, $0.4^2$.
Oct/Nov 2016
the number that is a multiple of 7.
Oct/Nov 2016
Write down one factor of 24 that is a square number.
Oct/Nov 2016
Calculate $\sqrt{2 + \frac{0.2}{1.7 - 0.9}}$.
Oct/Nov 2017
State the value of $12^0$.
Oct/Nov 2017
Calculate the value of $4.1^3$.
Oct/Nov 2018
Find the numerical value of $24^2$.
Oct/Nov 2019
Calculate the value of $\frac{5}{8} + \sqrt[3]{340}$.
Oct/Nov 2019
Calculate the expression $\sqrt{256^{0.25}} + 4 \times 8$.
Oct/Nov 2019
Calculate the value of $\sqrt{\frac{1}{0.01} - 8^2}$.
Oct/Nov 2020
Calculate the value of $\dfrac{4}{\sqrt{0.0025}}$.
Oct/Nov 2020
State the cube number that is above 50 but below 100.
Oct/Nov 2020
Let $N = 2^4 \times 3 \times 7^5$. The relation $PN = K$ holds, with $P$ an integer and $K$ a square number.
Oct/Nov 2020
Calculate the value of $\frac{4}{\sqrt{0.0025}}$.
Oct/Nov 2020
What is the value of $\sqrt{345.96}$?
Oct/Nov 2021
Calculate the value of $\dfrac{4.87 - 2.7}{-0.2 + \sqrt[3]{0.729}}$.
Oct/Nov 2021
Calculate the value of $\sqrt[4]{\frac{39}{16}}$.
Oct/Nov 2021
Using the list, write down the square root of 289.
Oct/Nov 2021
Write six hundred and three thousand eight hundred and twenty-one in figures.
Oct/Nov 2021
Determine the value of $\sqrt{53.29}$.
Oct/Nov 2022
Calculate the value of $\sqrt{15}+\frac{4.8}{2.2}$.
Oct/Nov 2022
Simplify the expression $(3125x^{3125})^{\frac{1}{5}}$.
Oct/Nov 2022
Determine the total of $3^2$ and $-3^2$.
Oct/Nov 2022
120, 121, 149, 164, 216
Oct/Nov 2022
Calculate the value of $\sqrt{15} + \frac{4.8}{2.2}$.
Oct/Nov 2022
List every factor of 68.
Oct/Nov 2022
Determine the value of $\sqrt[3]{5832}$.
Oct/Nov 2023
The numbers listed are 61, 63, 64, 66, 68 and 69.
Oct/Nov 2023
Calculate $\sqrt[3]{1 + 10.9 \times 0.4^2}$.
Oct/Nov 2024
Write 845024 using words.
Oct/Nov 2024
State the value of $\sqrt{144}$.
Oct/Nov 2025
Anna picks a number, multiplies it by 2, and then takes the square root. The result is 12.
Oct/Nov 2025
$(3-\sqrt5)(2+3\sqrt5)=a+b\sqrt5$. Find $a$ and $b$.
Oct/Nov 2025
Simplify the expression $\sqrt{125}-\sqrt{20}$.
Oct/Nov 2025
Find $\sqrt{1.96}$.
Oct/Nov 2025
Calculate the value of $\sqrt{361}+1$.
Oct/Nov 2025
Calculate the value of $\sqrt{\frac{8.4^2+9.3}{26.5}}$.
Oct/Nov 2025
State the reciprocal of 8.
Oct/Nov 2025
Calculate $(3.5^2-2.2^3)^{\frac14}$.
Oct/Nov 2025