[tex]\sf {\green {\underline {\red{\underline {♛ʙʀᴀɪɴʟʏ༊᭄ǫᴜᴇsᴛɪᴏɴ♛࿐ :-}}}}}[/tex]
[tex]\ \orange { \bold{ \underbrace{ \overbrace{RATIONALISE}}}}[/tex]
1. √5/√3+√2
2. 2+√3/√7+√3
3. 4/√7+√3
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[tex]\sf {\green {\underline {\red{\underline {♛ʙʀᴀɪɴʟʏ༊᭄ǫᴜᴇsᴛɪᴏɴ♛࿐ :-}}}}}[/tex]
[tex]\ \orange { \bold{ \underbrace{ \overbrace{RATIONALISE}}}}[/tex]
1. √5/√3+√2
2. 2+√3/√7+√3
3. 4/√7+√3
✧═══════•❁❀❁•════════✧
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Answer:
To rationalize these expressions, you want to eliminate the square roots from the denominators. You can do this by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial (a + b) is (a - b). Here's how to rationalize each expression:
1. √5 / (√3 + √2)
Multiply the numerator and denominator by the conjugate of the denominator, which is (√3 - √2):
[√5 * (√3 - √2)] / [(√3 + √2) * (√3 - √2)]
Simplify the denominator:
= (√5 * √3 - √5 * √2) / (3 - 2)
= (√15 - √10) / 1
= √15 - √10
2. (2 + √3) / (√7 + √3)
Multiply the numerator and denominator by the conjugate of the denominator, which is (√7 - √3):
[(2 + √3) * (√7 - √3)] / [(√7 + √3) * (√7 - √3)]
Simplify the denominator:
= (2√7 - 2√3 + 3) / (7 - 3)
= (2√7 - 2√3 + 3) / 4
= (1/2)√7 - (1/2)√3 + 3/4
3. 4 / (√7 + √3)
Multiply the numerator and denominator by the conjugate of the denominator, which is (√7 - √3):
[4 * (√7 - √3)] / [(√7 + √3) * (√7 - √3)]
Simplify the denominator:
= (4√7 - 4√3) / (7 - 3)
= (4√7 - 4√3) / 4
= √7 - √3