SIMPLIFY:
5 ROOT OF 6X +4 ROOT OF 6X
IS THE ROOT OF 77 IRRATIONAL OR RATIONAL?
SIMPLIFY:
8 + ROOT OF 24 DIVIDED BY 2
IS THE ROOT OF 49/100 RATIONAL OR IRRATIONAL AND IS THE ROOT OF 121 RATIONAL OR IRRATONAL?
SIMPLIFY:
ROOT OF 3X/2
THANKS IN ADVANCE!!!I AM FLUNKING THIS MATH CLASS AND HAVE THREE WEEKS TO GO TO PASS...
You need a tutor for the final three weeks. These are just about as simple as they get. Don't wait.
I'm here to help! Let's break down and simplify the expressions you provided, and then determine whether the given roots are rational or irrational.
1. Simplifying "5√(6x) + 4√(6x)":
First, notice that both terms have the same radical (√(6x)). You can combine like terms by adding the coefficients. In this case, the coefficients are 5 and 4:
5√(6x) + 4√(6x) = (5 + 4)√(6x) = 9√(6x)
So, the simplified expression is 9√(6x).
2. Determining whether √77 is rational or irrational:
To determine whether a root is rational or irrational, we need to check if the number inside the root (√77) is a perfect square. In this case, 77 is not a perfect square since it cannot be expressed as the square of an integer. Therefore, √77 is an irrational number.
3. Simplifying "8 + √24 ÷ 2":
To simplify this expression, start by simplifying the root (√24):
√24 can be written as √(4 × 6). Notice that 4 is a perfect square, so it can be taken out of the root.
√24 = √(4 × 6) = 2√6
Now, substitute this back into the original expression:
8 + √24 ÷ 2 = 8 + (2√6) ÷ 2
Next, divide 2√6 by 2:
8 + (2√6) ÷ 2 = 8 + √6
So, the simplified expression is 8 + √6.
4. Determining whether √(49/100) and √121 are rational or irrational:
To determine if a square root is rational or irrational, we need to check if the number inside the root is a perfect square.
a) √(49/100):
Begin by simplifying the fraction inside the root:
√(49/100) = √(7^2/10^2)
Both 7 and 10 are perfect squares, so the root can be simplified further:
√(7^2/10^2) = 7/10
Since 7/10 is a rational number, √(49/100) is also rational.
b) √121:
121 is a perfect square because it can be expressed as 11^2.
Therefore, √121 is rational.
So, both √(49/100) and √121 are rational numbers.
5. Simplifying "√(3x/2)":
To simplify this expression, we can apply the rationalizing technique. Multiply both the numerator and denominator by √2:
√(3x/2) × √2/√2 = √(3x/2) × √2/√2
Simplifying the numerator:
√(3x/2) × √2 = √(3x * 2) = √(6x)
Therefore, the simplified expression is √(6x).
I hope this helps! Remember, if you're struggling with math, it's a good idea to seek help from a tutor or teacher as soon as possible. Don't hesitate to ask further questions if needed.
I'm here to help! Let's break down each question step by step:
1. SIMPLIFY: 5 ROOT OF 6X + 4 ROOT OF 6X
To simplify this expression, notice that both terms have the same square root of 6x. We can combine like terms by adding their coefficients:
5 ROOT OF 6X + 4 ROOT OF 6X = (5 + 4) ROOT OF 6X = 9 ROOT OF 6X
2. IS THE ROOT OF 77 IRRATIONAL OR RATIONAL?
To determine whether the square root of 77 is rational or irrational, we need to check if 77 has any perfect square factors.
Since 77 is not a perfect square and it cannot be written as the ratio of two integers, the square root of 77 is an irrational number.
3. SIMPLIFY: 8 + ROOT OF 24 DIVIDED BY 2
To simplify this expression, let's start by simplifying the square root of 24:
ROOT OF 24 = ROOT OF (4 * 6) = ROOT OF 4 * ROOT OF 6 = 2 * ROOT OF 6
Now, we can simplify the entire expression:
8 + ROOT OF 24 DIVIDED BY 2 = 8 + (2 * ROOT OF 6) / 2 = 8 + ROOT OF 6
4. IS THE ROOT OF 49/100 RATIONAL OR IRRATIONAL AND IS THE ROOT OF 121 RATIONAL OR IRRATONAL?
To determine whether the square root of a fraction is rational or irrational, we need to simplify the fraction first:
ROOT OF 49/100 = ROOT OF (49/100) = ROOT OF 49 / ROOT OF 100 = 7/10
Since 7/10 is a rational number, the square root of 49/100 is rational.
Now, let's find the square root of 121:
ROOT OF 121 = 11
Since 11 is an integer and can be expressed as the ratio of two integers, the square root of 121 is a rational number.
5. SIMPLIFY: ROOT OF 3X/2
To simplify this expression, we can rewrite it as:
ROOT OF (3X/2) = (ROOT OF 3X) / (ROOT OF 2)
Simplifying each square root separately:
ROOT OF 3X / ROOT OF 2 = ROOT OF (3X/2)
Therefore, the simplified form of the square root of 3X/2 is the same as the original expression.
Remember, if you're struggling with your math class, it's important to seek help from a tutor or teacher as soon as possible. They can provide guidance and support to help you succeed in your studies. Good luck!