Rationalize the Denominator
Read this topicExplanations 5
- Multiply a radical expression by its conjugate to simplify Radicals are complex and messy all the time, but they're easier to handle in some places than others. For example, an …
By Zora Gilbert, Benjamin Qi, Moor Xu, Alex Federspiel, Anusha Rahman
- Rationalizing the Denominator To rationalize a denominator, you need to multiply the top and bottom by the conjugate of the denominator. A conjugate is the same two term express…
By Alex Federspiel, Amy Feraco, Caroline K
- (Video) Rationalize the Denominator by PatrickJMT Rationalize the denominator Your first instinct may be to wonder why we rationalize the denominator. A lot of the time, the sta…
By Ben Ferrara, Alex Federspiel, Anusha Rahman
- Rationalize Denominator with Conjugates To simplify expressions that have a root in the denominator we multiply the numerator and denominator by the conjugate. The conjugate is …
By Amy Feraco, Anusha Rahman
- Rationalize the Denominator The goal of this lesson is to learn how to simplify fractions with a radical in the denominator. Ultimately, we will get rid of the radical in the de…
By Trisha, Anusha Rahman
Problems 40
- Rationalize the denominator: 12/(13+46)12/(13+4\sqrt6)12/(13+46)
- Simplify. 111\frac{1}{\sqrt{11}}111
- Simplify. 3615\frac{3\sqrt{6}}{\sqrt{15}}1536
- Simplify 8xx4\frac{8x}{\sqrt[4]{x}}4x8x if x>0x>0x>0.
- Simplify. 613\frac{\sqrt{6}}{\sqrt{13}}136
- Simplify. 1803\frac{\sqrt{180}}{\sqrt{3}}3180
- Simplify. 16x3\sqrt{\frac{16x}{3}}316x
- What is 18−1218^{-\frac12}18−21 in radical form (or simplified if possible)?
- What is 455\frac{\sqrt{45}}{\sqrt{5}}545?
- Let α>0\alpha > 0α>0. What is 25αα\frac{\sqrt{25\alpha}}{\sqrt{\alpha}}α25α?
- Simplify the following expression: 26+52117+326\frac{\sqrt{26} + \sqrt{52}}{\sqrt{117} + 3\sqrt{26}}117+32626+52
- What is 11221\frac{\sqrt{112}}{\sqrt{21}}21112?
- What would you multiply the expression (3+5)(3+\sqrt5)(3+5) by to simplify the radical?
- What would you multiply (6+27)(6+\sqrt{27})(6+27) by to simplify the radical?
- Is this the right conjugation to simplify the expression? (7−3)(3−7)(\sqrt7-3)(3-\sqrt7)(7−3)(3−7)
- The conjugate of (12+2)(12+\sqrt2)(12+2) is:
- What do you get when you conjugate the radical (3x−11)(3x-\sqrt{11})(3x−11)
- What would you multiply by to simplify the expression 3x3+5x \dfrac{3x}{3+\sqrt5x}\;3+5x3x?
- True or False\text{True or False}True or False === When you multiply a fraction with a radical on the bottom by the conjugate, the goal is to get rid of all radicals in the expr…
- If you multiply 3x−23x-\sqrt23x−2 by the conjugate, what is the product?
- What do you get if you multiply −2+6-2+\sqrt6−2+6 by it's conjugate?
- After you Rationalize the denominator, what does the expression 3x2+7 \dfrac{3x}{2+\sqrt7}\;2+73x look like?
- After rationalizing the denominator, what will the expression 5−10+10 \dfrac{5}{-10+\sqrt{10}}\;−10+105 be?
- What would you multiply the expression xy2−tw−k \dfrac{xy^2-\sqrt{t}}{w-\sqrt{k}}\;w−kxy2−t by to rationalize the denominator?
- If you rationalize the denominator of the expression 3−53−20 \dfrac{3-\sqrt5}{3-\sqrt{20}}\;\;3−203−5 what does it look like after?
- Let aaa be a nonzero real number with a≠1a \not= 1a=1. Simplify: 1a+a+1a−a\frac{1}{a + \sqrt{a}} + \frac{1}{a - \sqrt{a}}a+a1+a−a1
- Let aaa be a nonzero real number with a≠1a \not= 1a=1. Simplify: a−aa+a\frac{a-\sqrt{a}}{a+\sqrt{a}}a+aa−a
- Remove the radical from the denominator: 63\frac{6}{\sqrt{3}}36
- Remove the radical from the denominator: 567\frac{56}{\sqrt{7}}756
- Remove the radical from the denominator: 312\frac{\sqrt{3}}{\sqrt{12}}123
- Remove the radical from the denominator: 4.52\frac{\sqrt{4.5}}{\sqrt{2}}24.5
- Why doesn't it change the value of a fraction when we multiply the numerator and denominator by a radical?
- If x<0x<0x<0, then 1−x3=?\frac{1}{\sqrt{-x^3}} = ?−x31=?
- 12=?\frac{1}{\sqrt2} = ?21=?
- 62=?\frac{6}{\sqrt2}=?26=?
- Rationalize the following expression: 3x3x3\frac{3\sqrt{x^{3}}}{\sqrt[3]{x}}3x3x3
- Rationalize the following expression: 7x2x\frac{7x^{2}}{\sqrt{x}}x7x2
- Rationalize the following expression: 22x\frac{2\sqrt{2}}{\sqrt{x}}x22
- Rationalize the following expression: 25x\frac{\sqrt{25}}{\sqrt{x}}x25
- Rationalize the following expression: 19x4\frac{19}{\sqrt[4]{x}}4x19