Simplify Radicals
Questions with Solutions for Grade 10
Grade 10 questions on how to simplify radicals expressions with solutions are presented.
In order to simplify radical expressions, you need to be aware of the following rules and properties of radicals
1) From definition of n th root(s) and principal root![equation 1](equations3/eq1.png)
Examples
![equation 3](equations3/eq3.png)
More examples on Roots of Real Numbers and Radicals .
2) Product (Multiplication) formula of radicals with equal indices is given by
![equation 4](equations3/eq4.png)
More examples on how to Multiply Radical Expressions .
3) Quotient (Division) formula of radicals with equal indices is given by
![equation 5](equations3/eq5.png)
More examples on how to Divide Radical Expressions .
4) You may add or subtract like radicals only
Example
![equation 6](equations3/eq6.png)
More examples on how to Add Radical Expressions .
5) You may rewrite expressions without radicals (to rationalize denominators) as follows
A) Example 1:
![equation 7](equations3/eq7.png)
B) Example 2:
![equation 9](equations3/eq8.png)
C) Example 3:
![equation 9](equations3/eq9.png)
More examples on how to Rationalize Denominators of Radical Expressions .
Questions
Rationalize and simplify the given expressions![equation 10](equations3/eq10.png)
Answers to the above questions
1)Write 128 and 32 as product/powers of prime factors: 128 = 2 7 , 32 = 2 5 hence
![equation 11](equations3/eq11.png)
2)
Use product rule to write that √2 √6 = √12
![equation 12](equations3/eq12.png)
3)
Write 14 and 63 as products of prime numbers 14 = 2 × 7 , 63 = 3 2 × 7 and substitute
![equation 13](equations3/eq13.png)
4)
Write 32 and 16 as products of prime numbers 32 = 2 5 , 16 = 2 4 and substitute
![equation 14](equations3/eq14.png)
5)
Write 64 as products of prime numbers 64 = 2 6 and substitute
![equation 15](equations3/eq15.png)
Rationalize the denominator by multiplying numerator and denominator by ( 3 √7) 2
![equation 16](equations3/eq16.png)
6)
Write 54 as products of prime numbers 54 = 2 × 3 3 and substitute
![equation 17](equations3/eq17.png)
7)
Multiply the denominator and numerator by the conjugate of the denominator
![equation 18](equations3/eq18.png)
Expand and simplify
![equation 19](equations3/eq19.png)
More Questions With Answers
Use all the rules and properties of radicals to rationalize and simplify the following expressions.![equation 20](equations3/eq20.png)
Solutions to the Above Questions
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Write 25 and 125 as the product of prime factors: 25 = 52 and 125 = 53, hence
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Write 64 and 16 as the product of prime factors: 64 = 26 and 16 = 24, hence
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Use product rule
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Convert the mixed number under the radical into a fraction and substitute
Use the division formula for radicals
Write 64 and 27 as product of prime factors, substitute and simplify
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Use the product formula and write 34 as the product of prime factors
Simplify
For √(17 x) and √(34 x) to be real numbers, x must be positive hence |x| = x
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Write the radicand as a square and simplify
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Write the radicand as the product of $2$ and a square and simplify
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Simplify the radicand
Write as the product of prime factors and simplify
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Since n is a positive integer, then N = 2 n + 1 is an odd integer. Hence
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Since n is a positive integer, then N = 2 n is an even integer. Hence
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Use division rule and simplify the radicand
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Multiply numerator and denominator by the conjugate of the denominator
Expand and simplify
Links and References
High School Math (Grades 10, 11 and 12) - Free Questions and Problems With AnswersMiddle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
More Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
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