\sqrt(60)-:2\sqrt(5)
To solve this expression, we must divide the square root of 60 by 2 times the square root of 5.
First, we simplify each term individually:
√60 can be simplified by factoring out the largest perfect square that divides evenly into 60:
√60 = √(2*2*3*5) = 2√15
2√5 remains the same.
Now, we divide the two terms:
(2√15) ÷ (2√5)
Since the denominators are the same, we can cancel them out, leaving us with:
√15 ÷ √5
When dividing square roots, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:
(√15 ÷ √5) * (√5 ÷ √5)
This simplifies to:
(√(15*5) ÷ √(5*5)) = √75 ÷ √25
Further simplifying within the square roots:
√75 = √(25*3) = 5√3
√25 = 5
So the final expression is:
5√3 ÷ 5
Since the 5s in the numerator and denominator cancel out, we are left with √3 as the simplified answer:
√(60)-:2√5 = √3
\sqrt(60)-:2\sqrt(5) A. \sqrt(30) / \sqrt(5) B. 12 / 2\sqrt(5) C. \sqrt(12) / 2 D. 12 / 2
To solve this expression, we can simplify each term individually and then divide them.
First, let's simplify √60. We can factor 60 into its prime factors:
√60 = √(2 * 2 * 3 * 5) = 2√15
Next, let's simplify 2√5. This term does not have any perfect square factors, so it remains as it is.
Now, we can divide the two terms:
(2√15) / (2√5)
The 2's in the numerator and denominator cancel out, leaving us with:
√15 / √5
To divide these two square root terms, we need to rationalize the denominator. This means multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √5 is -√5.
(√15 / √5) * (-√5 / -√5)
This simplifies to:
(-√(15*5) / (-√(5*5))) = (-√(75) / (-√(25)))
Further simplifying within the square roots:
-√75 = -√(25 * 3) = -5√3
-√25 = -5
So the final expression is:
-5√3 / -5
The negatives in the numerator and denominator cancel out, leaving us with:
√3
Therefore, the simplified answer is √3.
Correct answer: A. √(30) / √(5)
To simplify the expression \(\sqrt{60} - \frac{1}{2}\sqrt{5}\), we can follow these steps:
Step 1: Simplify the square root of 60.
\( \sqrt{60} = \sqrt{4 \cdot 15} = \sqrt{4} \cdot \sqrt{15} = 2 \sqrt{15} \)
Step 2: Substitute the simplified value of \(\sqrt{60}\) into the expression.
\( 2 \sqrt{15} - \frac{1}{2}\sqrt{5} \)
Step 3: Simplify the fraction \(\frac{1}{2}\sqrt{5}\) by multiplying the numerator and denominator by 2.
\( \frac{1}{2}\sqrt{5} = \frac{1 \cdot 2}{2 \cdot 2} \cdot \sqrt{5} = \frac{2}{4} \cdot \sqrt{5} = \frac{1}{2}\sqrt{5} \)
Step 4: Now subtract the simplified terms.
\( 2 \sqrt{15} - \frac{1}{2}\sqrt{5} = \boxed{ 2 \sqrt{15} - \frac{1}{2}\sqrt{5} } \)
To simplify the expression \(\sqrt{60} - \frac{{\sqrt{5}}}{{2}}\), we can simplify each term separately.
First, let's simplify \(\sqrt{60}\).
To find the value of \(\sqrt{60}\), we start by factoring 60 into its prime factors: \(60 = 2 \times 2 \times 3 \times 5\).
Since there is a perfect square, \(2 \times 2 = 4\), we can rewrite \(\sqrt{60}\) as \(\sqrt{4 \times 3 \times 5}\).
Using the square root property \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\), we can split \(\sqrt{4 \times 3 \times 5}\) into \(\sqrt{4} \times \sqrt{3} \times \sqrt{5}\), which simplifies to \(2 \sqrt{15}\).
Now let's simplify \(\frac{{\sqrt{5}}}{{2}}\).
Since we want to divide \(\sqrt{5}\) by 2, we just keep the numerator as is and write the denominator as 2: \(\frac{{\sqrt{5}}}{{2}}\).
Now we can rewrite the entire expression using the simplified terms:
\(\sqrt{60} - \frac{{\sqrt{5}}}{{2}} = 2 \sqrt{15} - \frac{{\sqrt{5}}}{{2}}\).
This is the simplified form of the given expression, and it cannot be simplified further.