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What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
When is written in simplest radical form which value remains under the radical?
The radicand is the value under the radical symbol.
What is the square root of -52?
No negative number can have a real square root.When you acquire enough math to work with imaginary numbers,you'll be able to express the square root of -52 as j7.2111 (rounded).
The expression radical 3x is equivalent to the expression x radical 3?
Radical (3x) = radical(x) * radical(3).
What is -3 radical 2 radical 50?
-3*radical(2)*radical(50) = -3*radical(2*50) = -3*radical(100) = -3*10 = -30
You can only use conjugates to rationalize the denominator when the denominator contains one radical term?
No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
Can you rationalize the denominator using conjugates even when the denominator contains two radical terms?
Yes. For example, the conjugate of (square root of 2 + square root of 3) is (square root of 2 - square root of 3).
Can you rationalize a denominator with more than one radical term?
Yes, you can.
Discuss the use of conjugates in radical problems?
Conjugates are often used in radical problems to simplify expressions and remove radicals from denominators. When dealing with a fraction that has a radical in the denominator, multiplying both the numerator and denominator by the conjugate of the denominator allows for the application of the difference of squares formula, which eliminates the radical. This technique simplifies calculations and makes it easier to work with rational expressions. Additionally, using conjugates can help in solving equations involving radicals more efficiently.
How do you rationalize the denominator of a radical expression that has two terms in the denominator?
You multiply the numerator and the denominator by the "conjugate" of the denominator. For example, if the denominator is root(2) + root(3), you multiply top and bottom by root(2) - root(3). This will eliminate the roots in the denonimator.
How do you rationalize radical 7?
If you are referring to 1/sqrt7 then you multiply the numerator and denominator by sqrt7 over sqrt7. 1 = (1)sqrt7 = sqrt7 sqrt7 (sqrt7)sqrt(7) 7
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
When is a radical in simplest form?
when there is no radical in the denominator
When dividing radicalsif there is a radical in the denominator you have to?
Rationalise the denominator.
What is it called to get the radical out of the denominator in algebra?
Rationalising the denominator.
How do you simplify 3 over the square root of 2?
You can rationalize the denominator by multiplying this fraction by a fractional form of one in radical form. 3/sqrt(2) * sqrt(2)/sqrt(2) = 3sqrt(2)/2 ----------------
Does a radical in its simplest from contain a radical in its denominator?
No. One of the rules for "simplest form" is that there may be no radical in the denominator. To fix this, multiply top and bottom of the fraction by the radical denominator. For example, ( 1 / √2) = (1 / √2)(√2 / √2) = (√2 / 2)
