1. which number below is irrational?
a)√4/9 b) √20 c)√121
Why is the number you chose irrational?
2. express in simplest form:
√48-5√27+2√75
3. solve for x: (√x+2)-3=0
1. The number that is irrational is b) √20.
The reason why √20 is irrational is that it cannot be written as a fraction or a ratio of two integers. When √20 is simplified, it becomes √(4*5) = 2√5. Since √5 is an irrational number, 2√5 is also irrational.
2. To express √48 - 5√27 + 2√75 in the simplest form, we need to simplify each square root term and combine like terms.
√48 can be simplified to 4√3 because 48 can be factored into 16 and 3.
√27 can be simplified to 3√3 because 27 can be factored into 9 and 3.
√75 can be simplified to 5√3 because 75 can be factored into 25 and 3.
Now, substituting the simplified values back into the expression:
4√3 - 5(3√3) + 2(5√3)
= 4√3 - 15√3 + 10√3
Combining like terms, we get:
(4 - 15 + 10)√3
= -1√3
= -√3
So, the expression √48 - 5√27 + 2√75 in simplest form is -√3.
3. To solve (√x+2) - 3 = 0 for x, we can follow these steps:
Add 3 to both sides of the equation to isolate the square root term:
(√x+2) + 3 = 0 + 3
√x + 5 = 3
Next, subtract 5 from both sides of the equation:
√x + 5 - 5 = 3 - 5
√x = -2
Now, square both sides of the equation to eliminate the square root:
(√x)^2 = (-2)^2
x = 4
Therefore, the solution to (√x+2) - 3 = 0 is x = 4.
1. To determine which number below is irrational, we need to understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a fraction of two integers and cannot be written as a terminating or repeating decimal.
a) The square root of 4/9 can be simplified to √(2/3), which is a rational number because it can be expressed as a fraction.
b) The square root of 20 is not a perfect square, so we need to determine if it can be simplified. By factoring it, we get √(4 * 5), which can be written as 2√5. Since the square root of 5 is irrational, the number 2√5 is also irrational.
c) The square root of 121 is a perfect square, which simplifies to 11. This is a rational number.
The number that we chose as irrational is option b) √20, which simplifies to 2√5. It is irrational because it cannot be expressed as a fraction and it is not a perfect square.
2. To express √48 - 5√27 + 2√75 in simplest form, we need to simplify each square root separately and combine like terms.
√48 can be simplified as √(16 * 3), which is equal to 4√3.
√27 can be simplified as √(9 * 3), which is equal to 3√3.
√75 can be simplified as √(25 * 3), which is equal to 5√3.
Now, let's substitute the simplified forms back into the original expression:
4√3 - 5(3√3) + 2(5√3)
= 4√3 - 15√3 + 10√3
Now, we can combine like terms:
(4 - 15 + 10)√3
= -1√3
Therefore, the expression √48 - 5√27 + 2√75 simplifies to -√3 in simplest form.
3. To solve for x in the equation (√x + 2) - 3 = 0, we need to isolate the square root term and then square both sides of the equation to eliminate the square root.
Let's go through the steps:
(√x + 2) - 3 = 0
√x + 2 = 3
√x = 3 - 2
√x = 1
Now, we square both sides to remove the square root:
(√x)^2 = 1^2
x = 1
Therefore, the solution for x is x = 1.
1. Which numbers are NOT perfect squares?
2. √48-5√27+2√75
= √16√3 - 5√9√3 + 2√25√3
= 4√3 - 15√3 + 10√3
= -√3
3. I will assume you meant
√(x+2) - 3 = 0
then √(x+2) = 3
square both sides
x+2 = 9
x = 7
since we squared, we MUSYT verify all answers.
if x=7
LS = √(7+2) - 3
= √9 - 3
= 0
= RS
so x = 7