Mipango

Kikokotoo cha Kipeuo cha Pili na Kurahisisha Vipeuo

Kipeuo cha pili cha 65 ni kipi? √65 ≈ 8.062258, na hakirahisishiki kwa sababu 65 haina kipengele cha mraba. Kikokotoo hiki kinatafuta kipeuo chochote na kukiandika katika umbo rahisi zaidi, kwa mfano √180 = 6√5.

Namba nzima, desimali au sehemu kama 2/3

Tokeo

Weka thamani kisha bonyeza Kokotoa ili kuona tokeo.

Fomula

a2b=ab\sqrt{a^2 b} = a\sqrt{b}

Take square factors out of the root: √72 = √(36 × 2) = 6√2.

anbn=abn\sqrt[n]{a^n b} = a\sqrt[n]{b}

For an nth root, take out factors that are perfect nth powers.

Jinsi ya kutumia kikokotoo hiki

  1. Enter the number and choose which root you want.
  2. Press Calculate to get the simplified exact root and its decimal value.

Mifano iliyotatuliwa

The square root of 72

72 = 36 × 2, and 36 = 6² is a perfect square.

√72 = √(6² × 2) = 6√2 ≈ 8.485281.

The square root of 65

65 = 5 × 13. Neither factor is a perfect square, so √65 is already in simplest radical form.

√65 lies between √64 = 8 and √81 = 9, very close to 8: √65 ≈ 8.062258.

Simplify a cube root: ∛54

Choose the cube root. 54 = 27 × 2, and 27 = 3³ is a perfect cube.

∛54 = ∛27 × ∛2 = 3∛2 ≈ 3.779763.

Makosa ya kawaida

  • Not using the largest square factor: √180 = 2√45 is true but unfinished — 45 still contains 9. The simplest form is 6√5.
  • Splitting a sum: √(9 + 16) is 5, not √9 + √16 = 7.
  • Treating the decimal as exact: √65 ≈ 8.062258 is rounded; √65 is the exact value.

Maswali yanayoulizwa mara kwa mara

How do you simplify √180?

180 = 36 × 5, so √180 = 6√5 ≈ 13.416408 in simplest radical form.

What is the square root of 2116?

46, because 46 × 46 = 2116. It is a perfect square, so the root is a whole number.

What is the square root of x⁶?

√(x⁶) = |x³|, because (x³)² = x⁶. For x ≥ 0 that is simply x³. This calculator works with numbers; the algebra calculator handles expressions with letters.

Why is the answer written as 6√2 instead of a decimal?

√2 never ends or repeats, so 6√2 is the exact answer. The decimal shown with it is rounded.

Can I take the root of a negative number?

Odd roots, yes: ∛(−27) = −3. Even roots (square, 4th, …) of a negative number are not real numbers.

Jifunze zaidi