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Algebra

Squares and square rootsAlgebra

Estimating square rootsBasic Math

Prime factorizationAlgebra

Square and square roots- Home
- UK Year 10 Maths
- Surds

Still Confused?

Try reviewing these fundamentals first.

Algebra

Squares and square rootsAlgebra

Estimating square rootsBasic Math

Prime factorizationAlgebra

Square and square rootsStill Confused?

Try reviewing these fundamentals first.

Algebra

Squares and square rootsAlgebra

Estimating square rootsBasic Math

Prime factorizationAlgebra

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- Lesson: 2a1:56
- Lesson: 2b1:00
- Lesson: 2c1:11

Whenever we see "roots", let it be cubic roots or square roots, we know for sure that we will need to do prime factorization to find out the prime factors of the numbers. In this section, we use factors and multiples to find perfect cube whole numbers and cubic roots.

Basic concepts: Squares and square roots, Estimating square roots, Prime factorization, Square and square roots,

Related concepts: Conversions involve squares and cubic, Operations with radicals, Conversion between entire radicals and mixed radicals,

To cube: Raise the number to the third power

Ex: ${3^3}$ $= 3\times 3\times 3 = 27$

${6^3}$ = $6\times 6\times 6 = 216$

To cube root: Finding the three identical factors

Ex: ${^3}\sqrt{64}$ = ${^3}\sqrt{4\times 4\times 4}$ = 4

${^3}\sqrt{125}$ = ${^3}\sqrt{5\times 5\times 5}$ = 5

Perfect Cubes: ${0^3}$= 0

${1^3}$ = 1

${2^3}$ = 8

${3^3}$ = 27

${4^3}$ = 64

${5^3}$ = 125

${6^3}$ = 216

${7^3}$ = 343

${8^3}$ = 512

${9^3}$ = 729

${10^3}$ = 1000

Ex: ${3^3}$ $= 3\times 3\times 3 = 27$

${6^3}$ = $6\times 6\times 6 = 216$

To cube root: Finding the three identical factors

Ex: ${^3}\sqrt{64}$ = ${^3}\sqrt{4\times 4\times 4}$ = 4

${^3}\sqrt{125}$ = ${^3}\sqrt{5\times 5\times 5}$ = 5

Perfect Cubes: ${0^3}$= 0

${1^3}$ = 1

${2^3}$ = 8

${3^3}$ = 27

${4^3}$ = 64

${5^3}$ = 125

${6^3}$ = 216

${7^3}$ = 343

${8^3}$ = 512

${9^3}$ = 729

${10^3}$ = 1000

- 1.Understanding the negative cube roots of the followinga)${^3}\sqrt{27}$ - ${^3}\sqrt{27}$${^3}\sqrt{-27}$
- 2.Find the cube rootsa)${^3}\sqrt{-4913}$b)${^3}\sqrt{1331}$c)$-{^3}\sqrt{2197}$

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