Math Tests - mathematics practice questions

Numerical expressions with roots and exponents

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Simplifying square roots

To simplify roots you can use Product Property of Square Roots:

$$√{a×b}=√a×√b$$

At first, find the perfect square inside the square root:

$$√24;→;24=2×2×3×2=4×6$$
$$√24=√{4×6}=√4×√6=2×√6$$

This can be written as 2√6

You can also use these formulae:

$$a^2=a×a$$

$$a^1=a$$

$$a^0=1$$

$$a^{−1}=1/a$$

$$a^{−n}=1/{a^n}$$

$$a^m×a^n=a^m a^n=a^{(m+n)}$$

$${a^m}/{a^n}=a^{m−n}$$

$$(a^m)^n=a^{(m×n)}$$

$$a^{1/n}=√^{n}a$$

$$√^n{a}√^n{b} = √^n{ab}$$

$$√{ab} = √a×√b$$

$$√{a/b}=√a/√b$$

$$(a/b)^2=a^2/b^2$$

   
   

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