Just for reference √ = square root
Evaluate the following expressions:
a) 3√12 - 7√75
b) 1 3/5 + 4/-15
c) -3 + (-5) +3 (-5)
d) 3y+6/4 - y-3/2 = 3y/4
I will do a), the only one with a square root
a)
3√12 - 7√75
= 3(2√3) - 7(5√3) = -29√3
b) and c) are simple arithmetic questions
d) I have a feeling that your question should say
(3y+6)/4 - (y-3)/2 = 3y/4
in any case, multiply each term by 4 and it becomes a simple equation.
but how did you do a? im so confused
To evaluate the given expressions, we'll follow the order of operations (PEMDAS/BODMAS) and simplify each expression step by step.
a) 3√12 - 7√75:
To evaluate this expression, we need to simplify the square roots first by finding the prime factors inside the radicals:
√12 = √(2 * 2 * 3) = 2√3
√75 = √(3 * 5 * 5) = 5√3
Now we can substitute these simplified values back into the original expression:
3√12 - 7√75 = 3(2√3) - 7(5√3)
Next, we distribute the coefficients:
= 6√3 - 35√3
Now, we can combine like terms:
= (6 - 35)√3
Finally, solving for the coefficient:
= -29√3
Therefore, the value of a) 3√12 - 7√75 is -29√3.
b) 1 3/5 + 4/-15:
To add these two fractions, we need to have a common denominator:
1 3/5 = (5 * 1) + 3/5 = 5 + 3/5
Performing the addition of the whole numbers, we get:
= 8/5
Therefore, the value of b) 1 3/5 + 4/-15 is 8/5.
c) -3 + (-5) + 3(-5):
We'll start by performing the multiplication:
3(-5) = -15
Now we can substitute the simplified values back into the expression:
-3 + (-5) + (-15)
Next, we can combine the like terms:
= -3 - 5 - 15
Now, we can perform the addition:
= -23
Therefore, the value of c) -3 + (-5) + 3(-5) is -23.
d) 3y+6/4 - y-3/2 = 3y/4:
To solve this equation, we'll begin by applying the distributive property to simplify the expression:
3y + 6/4 - y - 3/2 = 3y/4
Next, we'll convert the fractions to have a common denominator:
6/4 = 3/2
Now, we substitute these values back into the original equation:
3y + 3/2 - y - 3/2 = 3y/4
Combine like terms:
2y = 3y/4
To solve for y, we'll isolate the variable y by multiplying both sides of the equation by 4:
4(2y) = 4(3y/4)
This simplifies to:
8y = 3y
Now, we'll isolate the y terms by subtracting 3y from both sides:
8y - 3y = 0
Combine like terms:
5y = 0
Finally, we have y = 0 as the solution to the equation.
Therefore, the value of d) 3y+6/4 - y-3/2 = 3y/4 is y = 0.