Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let x=sqrt(7+sqrt(7+sqrt(7+dots)))

Let x=7+7+7+… x=\sqrt{7+\sqrt{7+\sqrt{7+\ldots}}}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Evaluate radical expressionsright chevron icon

Full solution

Q. Let x=7+7+7+… x=\sqrt{7+\sqrt{7+\sqrt{7+\ldots}}}
  1. Assume xx equals expression: Let's assume xx equals the entire expression. So, x=7+7+7+….x = \sqrt{7 + \sqrt{7 + \sqrt{7 + \dots}}}.
  2. Substitute xx in square root: Since the expression inside the square root is the same as xx, we can substitute xx inside the square root. So, we get x=7+xx = \sqrt{7 + x}.
  3. Square both sides: Now, we square both sides to get rid of the square root. This gives us x2=7+xx^2 = 7 + x.
  4. Rearrange to quadratic equation: Rearrange the equation to get a quadratic equation: x2−x−7=0x^2 - x - 7 = 0.
  5. Solve using quadratic formula: We can solve this quadratic equation using the quadratic formula, x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where a=1a = 1, b=−1b = -1, and c=−7c = -7.
  6. Plug values in formula: Plugging the values into the quadratic formula gives us x=1±1+4×72x = \frac{1 \pm \sqrt{1 + 4 \times 7}}{2}.
  7. Simplify square root: Simplify the expression under the square root: x=1±292x = \frac{1 \pm \sqrt{29}}{2}.
  8. Take positive solution: Since xx is the length and cannot be negative, we take the positive solution: x=1+292x = \frac{1 + \sqrt{29}}{2}.

More problems from Evaluate radical expressions

Question
Evaluate the expression for j=7 j = 7 .\newline2j= 2j = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the expression for y=4 y = 4 and z=5 z = 5 . \newline yz= yz = _____
Get tutor helpright-arrow

Posted 1 month ago

Question
Evaluate the expression for t=0 t = 0 .\newline∣−4−t∣=|-4 - t| = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Dale drew 88 pictures. Belle drew pp fewer pictures than Dale. Choose the expression that shows how many pictures Belle drew. \newlineChoices: \newline(A) 88\newline(B) p−8p - 8\newline(C) 8+p8 + p\newline(D) 8−p8 - p
Get tutor helpright-arrow

Posted 2 months ago

Question
Write an expression for the sequence of operations described below. subtract 55 from 66, then add ww to the result Do not simplify any part of the expression. ______
Get tutor helpright-arrow

Posted 2 months ago

Question
Write an expression for the operation described below. \newlinesubtract 44 from aa \newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
John baked 1212 cookies. Alice baked nn fewer cookies than John.\newline Choose the expression that shows how many cookies Alice baked.\newline Choices:\newline(A) 1212\newline(B) n−12n - 12\newline(C) 12+n12 + n\newline(D) 12−n12 - n
Get tutor helpright-arrow

Posted 3 months ago

Question
Emma read 1515 books. Lucas read bb fewer books than Emma. Choose the expression that shows how many books Lucas read.\newlineChoices:\newline(A) 1515\newline(B) b−15b - 15\newline(C) 15+b15 + b\newline(D) 15−b15 - b
Get tutor helpright-arrow

Posted 3 months ago

Question
Max ran 1010 miles. Sarah ran mm fewer miles than Max. Choose the expression that shows how many miles Sarah ran.\newlineChoices:\newline(A)10(A)10\newline(B)m−10(B)m - 10\newline(C)10+m(C)10 + m\newline(D)10−m(D)10 - m
Get tutor helpright-arrow

Posted 3 months ago

Question
Carlos wrote 2020 poems. Fiona wrote pp fewer poems than Carlos. Choose the expression that shows how many poems Fiona wrote.\newlineChoices:\newline(A) 2020\newline(B) p−20p - 20\newline(C) 20+p20 + p\newline(D) 20−p20 - p
Get tutor helpright-arrow

Posted 3 months ago

View all (28)