Radical Expressions
Math ⇒ Algebra
Radical Expressions starts at 9 and continues till grade 12.
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See sample questions for grade 12
Explain why \( \sqrt{a^2} = |a| \ ) and not simply a.
Express \( \sqrt[3]{8x^6} \ ) in simplest form.
Express \( \sqrt[4]{16x^8} \ ) in simplest form.
If \( \sqrt{2x+1} = 5 \), find the value of x.
If \( \sqrt{x} + 2 = 6 \), what is the value of x?
If \( \sqrt{x} = 7 \), what is the value of x?
If \( x = 4 \), what is the value of \( \sqrt{x+5} \ )?
Rationalize and simplify: \( \frac{2}{1-\sqrt{3}} \ )
Which of the following is equal to \( (\sqrt{3} + 2)(\sqrt{3} - 2) \ )?
(1) 3 - 4
(2) 3 + 4
(3) 9 - 4
(4) 3 - 2\sqrt{3}
Which of the following is equivalent to \( \sqrt{18} \ )?
(1) 3\sqrt{2}
(2) 2\sqrt{3}
(3) 6\sqrt{3}
(4) 9\sqrt{2}
Which of the following is NOT a radical expression?
(1) \( \sqrt{7} \ )
(2) \( 2x^{1/2} \ )
(3) \( x^2 + 3 \ )
(4) \( \sqrt[3]{x} \ )
Which of the following is the conjugate of \( 3 + \sqrt{2} \ )?
(1) 3 - \sqrt{2}
(2) 3 + \sqrt{2}
(3) -3 + \sqrt{2}
(4) 3 - 2\sqrt{2}
Fill in the blank: \( \sqrt{a^2} = |\underline{\hspace{1cm}}| \ )
Fill in the blank: \( \sqrt{a^2b^4} = |a|\underline{\hspace{1cm}} \ )
Fill in the blank: \( \sqrt{a^2b} = |a|\sqrt{\underline{\hspace{1cm}}} \ )
Fill in the blank: \( \sqrt{a} \times \sqrt{b} = \underline{\hspace{2cm}} \ )
True or False: \( \sqrt{16} = \pm 4 \ )
True or False: \( \sqrt{a^2} = a \) for all real numbers a.
True or False: \( \sqrt{a} \times \sqrt{a} = a \ ) for all real numbers a.
True or False: \( \sqrt{a} + \sqrt{b} = \sqrt{a+b} \ ) for all real numbers a and b.
