simplify the radical expression by rationalizing the denominator.
4/*21
* means square root
multiply top and bottom by sqrt(21)
To simplify the radical expression 4/√21 by rationalizing the denominator, we can multiply the numerator and denominator by √21. This is done to eliminate the radical in the denominator.
(4/√21) * (√21/√21)
Multiplying the numerators and denominators together gives us:
(4 * √21) / (√21 * √21)
Simplifying further:
(4√21) / (√(21*21))
The square root of (21*21) is equal to 21:
(4√21) / 21
Therefore, the simplified expression is 4√21/21.
To simplify the radical expression 4/√21 by rationalizing the denominator, follow these steps:
Step 1: Write the expression as a fraction: 4/√21.
Step 2: To rationalize the denominator, we need to eliminate the radical (√) in the denominator.
Step 3: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √21 is (-√21). Multiply both the numerator and denominator by (-√21):
(4/√21) * (-√21) / (-√21)
Step 4: Simplify the expression:
(-4√21) / (-1 * √21)
= (-4√21) / (-√21)
= 4
Therefore, the simplified radical expression after rationalizing the denominator is 4.