Simplify
¡Ô(7+2(1+¡Ô3)x(1+¡Ô5))
into the form of ¡Ôx + ¡Ôy +¡Ôz
¡Ô means square root
pls help
thx
It would help if you proofread your questions before you posted them.
Online "√" (v+option keys) is used to indicate square root.
√(7+2(1+√3)x(1+√5) has no reference to y or z.
I think he wants to reduce it to the sum of three roots.
Balancing parentheses, I figure it means:
√(7+2(1+√3)(1+√5))
√(7+2(1+√3+√5+√15))
√(10+2√3+2√5+2√15)
Looks hard. Did I get the parens right?
yes the question is right, it appears on my test paper.
To simplify the given expression, we will first evaluate the expression within the innermost parentheses, then simplify further using the distributive property.
Let's start with the innermost parentheses: (1+√3) and (1+√5).
Next, we can distribute the 2 to the terms inside the parentheses, resulting in:
2(1+√3) = 2 + 2√3
2(1+√5) = 2 + 2√5
Now, return to the original expression:
√(7+2(1+√3)(1+√5))
Replace the terms within the expression:
√(7 + (2 + 2√3)(2 + 2√5))
Now, distribute the terms using the FOIL method (multiply each term of the first expression by each term of the second expression):
√(7 + 2(2 + 2√5) + 2√3(2 + 2√5) + 2√3(2 + 2√5))
Simplify this further:
√(7 + 4 + 4√5 + 4√3 + 4√5 + 4√15)
Combine like terms:
√(15 + 8√5 + 4√3 + 4√15)
This expression cannot be simplified further into the form of √x + √y + √z, as it has multiple radical terms with different radicands (numbers inside the square root).