лестница длиной 2 5 м приставлена к стене так, что ее верхний конец находится на высоте 2,4 м от земли. На сколько сантиметров о
1 ответ:
Читайте также
Пользользуемся свойствами степеней:
![\sqrt[m]{ {a}^{n} } = {a}^{ \frac{n}{m} } \\](https://tex.z-dn.net/?f=+%5Csqrt%5Bm%5D%7B+%7Ba%7D%5E%7Bn%7D+%7D+%3D+%7Ba%7D%5E%7B+%5Cfrac%7Bn%7D%7Bm%7D+%7D+%5C%5C+)
![b \sqrt[m]{ {a}^{n} } = \sqrt[m]{ {b}^{m} \times {a}^{n} } \\](https://tex.z-dn.net/?f=b+%5Csqrt%5Bm%5D%7B+%7Ba%7D%5E%7Bn%7D+%7D+%3D+%5Csqrt%5Bm%5D%7B+%7Bb%7D%5E%7Bm%7D+%5Ctimes+%7Ba%7D%5E%7Bn%7D+%7D+%5C%5C+)
![\sqrt[m]{ \sqrt[n]{a} } = \sqrt[m \times n]{a} \\](https://tex.z-dn.net/?f=+%5Csqrt%5Bm%5D%7B+%5Csqrt%5Bn%5D%7Ba%7D+%7D+%3D+%5Csqrt%5Bm+%5Ctimes+n%5D%7Ba%7D+%5C%5C+)
![{ (\sqrt[m]{ {a}^{n} }) }^{k} = \sqrt[m]{ {a}^{n \times k} }](https://tex.z-dn.net/?f=+%7B+%28%5Csqrt%5Bm%5D%7B+%7Ba%7D%5E%7Bn%7D+%7D%29+%7D%5E%7Bk%7D+%3D+%5Csqrt%5Bm%5D%7B+%7Ba%7D%5E%7Bn+%5Ctimes+k%7D+%7D)
________________________________
![\sqrt[4]{x \sqrt[2]{x \sqrt[3]{x} } } = \sqrt[4]{ \sqrt[2]{ {x}^{2} \times x \sqrt[3]{x} } } = \sqrt[4]{ \sqrt[2]{ {x}^{3} \sqrt[3]{x} } } = \\ = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{ {x}^{9} \times x} } } = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{ {x}^{10} } } } = \sqrt[24]{ {x}^{10} } = \\ = \sqrt[24]{ {( \sqrt[5]{ {27}^{4} } )}^{10} } = \sqrt[24]{ \sqrt[5]{ {27}^{4 \times 10} } } = \sqrt[24]{ \sqrt[5]{ {27}^{40} } } = \\ = \sqrt[120]{ {27}^{40} } = {27}^{ \frac{40}{120} } = {27}^{ \frac{1}{3} } = {3}^{ 3 \times \frac{1}{3} } = 3 \\](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7Bx+%5Csqrt%5B2%5D%7Bx+%5Csqrt%5B3%5D%7Bx%7D+%7D+%7D+%3D+%5Csqrt%5B4%5D%7B+%5Csqrt%5B2%5D%7B+%7Bx%7D%5E%7B2%7D+%5Ctimes+x+%5Csqrt%5B3%5D%7Bx%7D+%7D+%7D+%3D+%5Csqrt%5B4%5D%7B+%5Csqrt%5B2%5D%7B+%7Bx%7D%5E%7B3%7D+%5Csqrt%5B3%5D%7Bx%7D+%7D+%7D+%3D+%5C%5C+%3D+%5Csqrt%5B4%5D%7B+%5Csqrt%5B2%5D%7B+%5Csqrt%5B3%5D%7B+%7Bx%7D%5E%7B9%7D+%5Ctimes+x%7D+%7D+%7D+%3D+%5Csqrt%5B4%5D%7B+%5Csqrt%5B2%5D%7B+%5Csqrt%5B3%5D%7B+%7Bx%7D%5E%7B10%7D+%7D+%7D+%7D+%3D+%5Csqrt%5B24%5D%7B+%7Bx%7D%5E%7B10%7D+%7D+%3D+%5C%5C+%3D+%5Csqrt%5B24%5D%7B+%7B%28+%5Csqrt%5B5%5D%7B+%7B27%7D%5E%7B4%7D+%7D+%29%7D%5E%7B10%7D+%7D+%3D+%5Csqrt%5B24%5D%7B+%5Csqrt%5B5%5D%7B+%7B27%7D%5E%7B4+%5Ctimes+10%7D+%7D+%7D+%3D+%5Csqrt%5B24%5D%7B+%5Csqrt%5B5%5D%7B+%7B27%7D%5E%7B40%7D+%7D+%7D+%3D+%5C%5C+%3D+%5Csqrt%5B120%5D%7B+%7B27%7D%5E%7B40%7D+%7D+%3D+%7B27%7D%5E%7B+%5Cfrac%7B40%7D%7B120%7D+%7D+%3D+%7B27%7D%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D+%3D+%7B3%7D%5E%7B+3+%5Ctimes+%5Cfrac%7B1%7D%7B3%7D+%7D+%3D+3+%5C%5C+)
ОТВЕТ: 3
________________________________
ОТВЕТ: 3