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Write each expression in simplest form by rationalizing the denominator (2 marks each)
a)
(2sqrt3+4)/(sqrt3)
b)
(sqrt3)/(sqrt5+2sqrt2)

$4$ . Write each expression in simplest form by rationalizing the denominator ( $2$ marks each) $\newline$ a) $\frac{2 \sqrt{3}+4}{\sqrt{3}}$ $\newline$ b) $\frac{\sqrt{3}}{\sqrt{5}+2 \sqrt{2}}$

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Simplify radical expressions using conjugates

Full solution

Q.

4

. Write each expression in simplest form by rationalizing the denominator (

2

marks each)

\newline

a)

\frac{2 \sqrt{3}+4}{\sqrt{3}}

\newline

b)

\frac{\sqrt{3}}{\sqrt{5}+2 \sqrt{2}}

Divide and Simplify: To simplify the expression $(2\sqrt{3}+4)/(\sqrt{3})$ , we can divide each term in the numerator by the denominator.
Rationalize Fraction: Now, we rationalize the remaining fraction by multiplying the numerator and denominator by $\sqrt{3}$ .
Combine with Whole Number: Combine the rationalized fraction with the whole number.
Use Conjugate to Rationalize: For the expression $(\sqrt{3})/(\sqrt{5}+2\sqrt{2})$ , we will use the conjugate of the denominator to rationalize it. $\newline$ The conjugate of $\sqrt{5}+2\sqrt{2}$ is $\sqrt{5}-2\sqrt{2}$ .
Multiply Numerators and Denominators: Multiply the numerators and denominators.
Simplify Denominator: Simplify the denominator using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ .
Distribute $\sqrt{3}$ : Distribute $\sqrt{3}$ in the numerator.
Make Denominator Positive: Since we have a negative denominator, we can multiply the numerator and denominator by $-1$ to make the denominator positive.

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