<div class="test"><pre><textarea>{"questions":[{"content":"Вычислите:$$\\sqrt{400}=$$[[choice-1]]","widgets":{"choice-1":{"type":"choice","options":["$20$","$200$","$40$"],"explanations":["$20^2=400$","$200^2=40\\space000$","$40^2=1\\space600$"],"answer":[0]}},"id":"0"},{"content":"Вычислите:$$\\sqrt{1.44}=$$[[choice-2]]","widgets":{"choice-2":{"type":"choice","options":["$1.2$","$0.12$","$0.14$"],"explanations":["$1.2^2=1.44$","$0.12^2=0.0144$","$0.14^2=0.0196$"],"answer":[0]}},"id":"0"},{"content":"Вычислите:$$\\sqrt{0.01}=$$[[choice-3]]","widgets":{"choice-3":{"type":"choice","options":["$0.1$","$0.01$","$1$"],"explanations":["$0.1^2=0.01$","$0.01^2=0.0001$","$1^2=1$"],"answer":[0]}},"id":"0"},{"content":"Найдите значение выражения:$$\\sqrt{\\frac{1}{25}}+7=$$[[fill_choice_big-77]][[image-1455]]","widgets":{"fill_choice_big-77":{"type":"fill_choice_big","options":["$7.2$","$6.8$","$32$"],"placeholder":0,"answer":0},"image-1455":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/03/arhitektor-stroitel-doska-chertezh-rulon-bumaga-3.svg","width":"400"}},"step":1,"hints":["Найдем значение квадратного корня:$$\\sqrt{\\frac{1}{25}}=\\sqrt{0.04}=0.2$$","Выполним сложение:$$0.2+7=7.2$$"],"id":"1"},{"content":"Найдите значение выражения:$$\\sqrt{1}-1=$$[[fill_choice_big-110]][[image-1520]]","widgets":{"fill_choice_big-110":{"type":"fill_choice_big","options":["$0$","$1$","$-1$"],"placeholder":0,"answer":0},"image-1520":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/mudrecz-kolonna-atom.svg","width":"400"}},"step":1,"hints":["Найдем значение квадратного корня:$$\\sqrt{1}=1$$","Выполним вычитание:$$1-1=0$$"],"id":"1"},{"content":"Найдите значение выражения:$$18+\\sqrt{\\frac{1 0\\space000}{1}}=$$[[fill_choice_big-191]][[image-1555]]","widgets":{"fill_choice_big-191":{"type":"fill_choice_big","options":["$118$","$1018$","$180$"],"placeholder":0,"answer":0},"image-1555":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/12/lawyer-01.svg","width":"400"}},"step":1,"hints":["Найдем значение квадратного корня:$$\\sqrt{\\frac{1 0\\space000}{1}}=\\sqrt{10\\space000}=100$$","Выполним сложение:$$18+100=118$$"],"id":"1"},{"content":"Упростите выражение:$$5\\sqrt{25}+8$$[[fill_choice_big-85]][[image-1664]]","widgets":{"fill_choice_big-85":{"type":"fill_choice_big","options":["$33$","$13$","$43$"],"placeholder":0,"answer":0},"image-1664":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/12/research-phase-1.svg","width":"400"}},"step":1,"hints":["Найдем корень из $25$:$$\\sqrt{25}=\\textcolor{blue}{5}$$","Выполним умножение:$$5\\cdot \\textcolor{blue}{5} = \\textcolor{darkgreen}{25}$$","Найдем сумму полученных чисел:$$\\textcolor{darkgreen}{25}+8=33$$"],"id":"2"},{"content":"Упростите выражение:$$\\frac{1}{2}\\sqrt{1.96}$$[[fill_choice_big-219]]","widgets":{"fill_choice_big-219":{"type":"fill_choice_big","options":["$0.7$","$0.8$","$8$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдем значение корня:$$\\sqrt{1.96}=1.4$$","Выполним умножение:$$\\frac{1}{2}\\cdot 1.4 = 0.7$$"],"id":"2"},{"content":"Упростите выражение:$$80-10\\sqrt{0.01}$$[[fill_choice_big-378]]","widgets":{"fill_choice_big-378":{"type":"fill_choice_big","options":["$79$","$79.9$","$70$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдем значение корня:$$\\sqrt{0.01}=0.1$$","Выполним умножение:$$10 \\cdot 0.1=1$$","Вычтем из $80$ полученное значение:$$80-1=79$$"],"id":"2"},{"content":"Решите уравнение:$$\\sqrt{y-2}=2$$[[fill_choice_big-585]]","widgets":{"fill_choice_big-585":{"type":"fill_choice_big","options":["$6$","$2$","$4$"],"placeholder":0,"answer":0}},"step":1,"hints":["Исходя из определения квадратного корня:$$y-2=2^2$$","Решим полученное уравнение:$$y\\textcolor{darkgreen}{-2}=\\textcolor{darkgreen}{4}$$ $$y=\\textcolor{darkgreen}{6}$$"],"id":"3"},{"content":"Решите уравнение:$$\\sqrt{y-1}=11$$[[fill_choice_big-782]]","widgets":{"fill_choice_big-782":{"type":"fill_choice_big","options":["$122$","$10$","$144$"],"placeholder":0,"answer":0}},"step":1,"hints":["Исходя из определения квадратного корня:$$y-1=11^2$$","Решим уравнение:$$y\\textcolor{darkgreen}{-1}=\\textcolor{darkgreen}{121}$$ $$y=\\textcolor{darkgreen}{122}$$"],"id":"3"},{"content":"Решите уравнение:$$\\sqrt{y+8}=8$$[[fill_choice_big-726]]","widgets":{"fill_choice_big-726":{"type":"fill_choice_big","options":["$56$","$0$","$63$"],"placeholder":0,"answer":0}},"step":1,"hints":["Исходя из определения квадратного корня:$$y+8=8^2$$","Решим уравнение:$$y+\\textcolor{darkgreen}{8}=\\textcolor{darkgreen}{64}$$ $$y=\\textcolor{darkgreen}{56}$$"],"id":"3"},{"content":"Найдите значение переменной $x$, при котором$$\\sqrt{x}=25$$[[fill_choice_big-1035]][[image-1741]]","widgets":{"fill_choice_big-1035":{"type":"fill_choice_big","options":["$625$","Таких значений $x$ не существует.","$5$"],"placeholder":0,"answer":0},"image-1741":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/12/big-x-concept-v3.svg","width":"400"}},"step":1,"hints":["Найдем такое число, корень из которого равен $25.$","$$\\sqrt{\\textcolor{darkgreen}{625}}=25$$"],"id":"4"},{"content":"Найдите значение переменной $x$, при котором$$\\sqrt{x}+1=0$$[[fill_choice_big-1008]][[image-1822]]","widgets":{"fill_choice_big-1008":{"type":"fill_choice_big","options":["Таких значений $x$ не существует.","$1$","$-1$"],"placeholder":0,"answer":0},"image-1822":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/10/lenivyi-lezhit-divan-kreslo-torsher.svg","width":"400"}},"step":1,"hints":["Перенесем $1$ за знак равно с противоположным знаком:$$\\sqrt{x}=-1$$","Квадратный корень из числа не может быть отрицательным, поэтому значений $x$, при котором $\\sqrt{x}=-1,$ не существует."],"id":"4"},{"content":"Найдите значение переменной $x$, при котором$$\\sqrt{x}-9=0$$[[fill_choice_big-260]][[image-1907]]","widgets":{"fill_choice_big-260":{"type":"fill_choice_big","options":["$81$","$3$","Таких значений $x$ не существует."],"placeholder":0,"answer":0},"image-1907":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/07/shestirenki-01.svg","width":"400"}},"step":1,"hints":["Перенесем $9$ за знак равно с противоположным знаком:$$\\sqrt{x}=9$$","Найдем такое число, корень из которого равен $9$:$$\\sqrt{\\textcolor{darkgreen}{81}}=9$$"],"id":"4"}]}</textarea></pre></div>