Solve a square root

Solve a square root

CONCEPTS

Radicals

• Used to indicate a root

• ⁿ√x reads, x radical n or the nth root of x. It can also be written x¹ᐟⁿ

EXAMPLES

• ²√3 = √3 = 3¹ᐟ² (The 2 does not need to be to the left of the root symbol √)

• ³√x = x¹ᐟ³

• ³√a⁵ = a⁵ᐟ³

PRACTICE PROBLEMS

Question 1 What is the smallest integer greater than √61?

-- Answer -- 8

7² = 49, 8² = 64

√61 < √64 => √61 < 8

Question 2 Simply √20 + √5

-- Answer -- 3√5

√20 + √5 = 20¹ᐟ² + 5¹ᐟ² = 4¹ᐟ² * 5¹ᐟ² + 5¹ᐟ² = 5¹ᐟ² (1 + 4¹ᐟ²) = √5 (1 + 2) = 3√5

ACT PRACTICE PROBLEMS

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