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Surds

The document discusses simplifying and evaluating expressions involving surds (irrational numbers expressed as the square root of a number). It includes examples of writing surds in the form k√m, combining like surds, evaluating surd expressions, expanding and simplifying expressions with surds, and rationalizing denominators containing surds. The document contains 8 sections with multiple parts providing practice with different surd operations and manipulations.

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Maria Gonzalez
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310 views3 pages

Surds

The document discusses simplifying and evaluating expressions involving surds (irrational numbers expressed as the square root of a number). It includes examples of writing surds in the form k√m, combining like surds, evaluating surd expressions, expanding and simplifying expressions with surds, and rationalizing denominators containing surds. The document contains 8 sections with multiple parts providing practice with different surd operations and manipulations.

Uploaded by

Maria Gonzalez
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Surds

1. Find the value of k in each of these

a)√ 8=k √2 b)√ 50=k √ 2 c)√ 98=k √ 2 d)√ 12=k √ 3


e)√ 300=k √ 3 f)√ 45=k √ 5 g)√ 125=k √ 5 h)√ 28=k √ 7

2. Simplify fully, write each in the form k √ m where k and m are both integers.

a)√ 20 b)√ 18 c)√ 32 d)√ 72


e)√ 162 f)√ 147 g)√ 256 h)√ 288

3. Write these as a single surd then evaluate

a)√ 20 × √ 5 b)√ 16 × √ 4 c)√ 27 × √ 3 d)√ 200 × √ 2


e)√ 24 × √ 6 f)√ 28 × √ 7 g)√ 6 × √ 8 × √ 3 h)√ 5 × √ 10× √ 2
4. Evaluate

a)2 √20 × 3 √ 5 b)4 √ 27 × 6 √ 3 c)5 √ 24 ×2 √ 6 d)3 √ 6 ×2 √ 8× 4 √ 3

5. Write as a single surd then evaluate

a)
√50 b)
√ 90 c)
√320 d)
√1000
√2 √10 √5 √10

e)
√32 × √ 4 f)
√ 35 × √5 g)
√ 48 × √ 8 h)
√ 30 × √ 12
√2 √7 √6 √2 × √5

6. Evaluate

8 √ 75 6 √ 160 2 √ 320 4 √72 ×3 √ 4


a) b) c) d)
√5 3 √ 10 4 √5 12 √ 2
7. Expand & Simplify

a)( 5+ √ 3 ) ( 6+ √ 3 ) b)( 4+ √ 2 ) ( 5−√ 2 ) c)( 7+ √ 5 ) ( 7−√ 5 ) d)( 2+ √ 3 ) ( 2+ √ 3 )

e)( 1+2 √ 5 )( 6 + √ 5 ) f)( 7−√ 2 )( 4−3 √ 2 ) g)( 2+ √ 2 ) ( 5−√ 8 ) h)( 6+ 3 √ 3 ) ( 6−3 √ 3 )

8. Rationalise the denominators

5 8 9 5
a) b) c) d)
√2 √2 √3 √5
1 8 3+ √ 2 6− √ 5
e) f) g) h)
1+ √ 2 2−√ 5 3−√ 2 6+ √ 5

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