<< Chapter < Page Chapter >> Page >

Adding square roots

Add 5 12 + 2 3 .

We can rewrite 5 12 as 5 4 · 3 . According the product rule, this becomes 5 4 3 . The square root of 4 is 2, so the expression becomes 5 ( 2 ) 3 , which is 10 3 . Now we can the terms have the same radicand so we can add.

10 3 + 2 3 = 12 3

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Subtracting square roots

Subtract 20 72 a 3 b 4 c 14 8 a 3 b 4 c .

Rewrite each term so they have equal radicands.

20 72 a 3 b 4 c = 20 9 4 2 a a 2 ( b 2 ) 2 c = 20 ( 3 ) ( 2 ) | a | b 2 2 a c = 120 | a | b 2 2 a c
14 8 a 3 b 4 c = 14 2 4 a a 2 ( b 2 ) 2 c = 14 ( 2 ) | a | b 2 2 a c = 28 | a | b 2 2 a c

Now the terms have the same radicand so we can subtract.

120 | a | b 2 2 a c 28 | a | b 2 2 a c = 92 | a | b 2 2 a c
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Subtract 3 80 x 4 45 x .

0

Got questions? Get instant answers now!

Rationalizing denominators

When an expression involving square root radicals is written in simplest form, it will not contain a radical in the denominator. We can remove radicals from the denominators of fractions using a process called rationalizing the denominator .

We know that multiplying by 1 does not change the value of an expression. We use this property of multiplication to change expressions that contain radicals in the denominator. To remove radicals from the denominators of fractions, multiply by the form of 1 that will eliminate the radical.

For a denominator containing a single term, multiply by the radical in the denominator over itself. In other words, if the denominator is b c , multiply by c c .

For a denominator containing the sum or difference of a rational and an irrational term, multiply the numerator and denominator by the conjugate of the denominator, which is found by changing the sign of the radical portion of the denominator. If the denominator is a + b c , then the conjugate is a b c .

Given an expression with a single square root radical term in the denominator, rationalize the denominator.

  1. Multiply the numerator and denominator by the radical in the denominator.
  2. Simplify.

Rationalizing a denominator containing a single term

Write 2 3 3 10 in simplest form.

The radical in the denominator is 10 . So multiply the fraction by 10 10 . Then simplify.

2 3 3 10 10 10      2 30 30             30 15
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Write 12 3 2 in simplest form.

6 6

Got questions? Get instant answers now!

Given an expression with a radical term and a constant in the denominator, rationalize the denominator.

  1. Find the conjugate of the denominator.
  2. Multiply the numerator and denominator by the conjugate.
  3. Use the distributive property.
  4. Simplify.

Rationalizing a denominator containing two terms

Write 4 1 + 5 in simplest form.

Begin by finding the conjugate of the denominator by writing the denominator and changing the sign. So the conjugate of 1 + 5 is 1 5 . Then multiply the fraction by 1 5 1 5 .

4 1 + 5 1 5 1 5 4 4 5 4 Use the distributive property . 5 1 Simplify .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Write 7 2 + 3 in simplest form.

14 −7 3

Got questions? Get instant answers now!

Using rational roots

Although square roots are the most common rational roots, we can also find cube roots, 4th roots, 5th roots, and more. Just as the square root function is the inverse of the squaring function, these roots are the inverse of their respective power functions. These functions can be useful when we need to determine the number that, when raised to a certain power, gives a certain number.

Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply
Practice Key Terms 6

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask